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PHXII03:CURRENT ELECTRICITY

357141 Two bars of radius $r$ and 2 $r$ are kept in contact as shown. An electric current $i$ is passed through the bars. Which one of the following is correct?
supporting img

1 Heat produced in bar

B C

is 4 times the heat produced in bar

A B

.

2 Potential difference across

A B

is 4 times that of across

B C

.

3 Electric field in both halves is equal.

4 Current density across

A B

is double that of cross

B C

.

Explanation:

Current flowing through both the bars is equal.
Now, the heat produced is given by
$H = I^{2} R t \Rightarrow H \propto R$
$\frac{H_{A B}}{H_{B C}} = \frac{R_{A B}}{R_{B C}} = \frac{{(1 / 2 r)}^{2}}{{(1 / r)}^{2}} = \frac{1}{4} (R \propto \frac{1}{r^{2}})$

PHXII03:CURRENT ELECTRICITY

357142 The supply voltage in a room is 120 $V$ . The resistance of the lead wires is $6 Ω$ . 60 $W$ bulb is already switched on. What is the decrease of voltage across the bulb when a 240 $W$ heater is switched on in parallel to the bulb?

1 13.3

V

2 Zero

3 2.9

V

4 10.4

V

Explanation:

The resistance of the bulb is
$R = \frac{120 \times 120}{60} = 240 Ω$
$R_{e q} = 240 + 6 = 246 Ω$
supporting img
$V_{1} = \frac{240}{246} \times 120 = 117.073 V$
After connecting the heater

$V_{2} = \frac{48}{54} \times 120 = 106.66 V$
$V_{1} - V_{2} = 10.04 V$

PHXII03:CURRENT ELECTRICITY

357143 Assertion :
The coil of a heater is cut into two equal halves and only one of them is used into heater. The heater will now require half the time to produce the same amount of heat.
Reason :
The heat produced is directly proportional to square of current.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The power (heat produced per unit time) in a heater is given by $P = V^{2} / R$ , where $V$ is the voltage and $R$ is the resistance. If the resistance is halved by using only one-half of the coil, the power is doubled $(P = V^{2} / (R / 2) = 2 V^{2} / R)$ . Since power is directly proportional to the square of the current $(P α I^{2})$ , using half of the coil will result in the same amount of heat being produced in half the time, as stated in the assertion. So correct option is (2).

PHXII03:CURRENT ELECTRICITY

357144 For ensuring dissipation of same energy in all three resistors $(R_{1}, R_{2}, R_{3})$ connected as shown in figure, their values must be related as
supporting img

1

R_{1} = R_{2} = R_{3}

2

R_{2} = R_{3}

and

R_{1} = 4 R_{2}

3

R_{2} = R_{3}

and

R_{1} = \frac{R_{2}}{4}

4

R_{1} = R_{2} + R_{3}

Explanation:

The voltage across $R_{2}$ and $R_{3}$ is same.
Therefore, for same energy loss according to $H = \frac{V^{2}}{R} t, R_{2}$ must be equal to $R_{3}$ .
$i . e .$ $R_{2} = R_{3}$
Again, the energy is same in all resistances.
$∴ i^{2} R_{1} t = i_{1}^{2} R_{2} t (1)$
and $i_{1} = \frac{R_{3}}{R_{2} + R_{3}} i = \frac{R_{3}}{R_{3} + R_{3}} i = \frac{1}{2} i (2)$
$[∵ R_{2} = R_{3}]$
Thus, $i^{2} R_{1} t = \frac{i^{2}}{4} R_{2} t$ [From Eqs. (1) and (2)]
$∴ R_{1} = \frac{R_{2}}{4}$
So, correct option is (3)

AIIMS - 2005

PHXII03:CURRENT ELECTRICITY

357145 Assertion :
KWhr is a commercial unit used for expressing consumed electric energy.
Reason :
Kilo-Watt hour is the unit of electric power.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$(k W h r)$ is a unit of electric energy. It is calculated by multiplying the power in kilowatts $(k W)$ by the time in hours. This unit is commonly used to measure and express the amount of electric energy consumed. So correct option is (3).

PHXII03:CURRENT ELECTRICITY

357141 Two bars of radius $r$ and 2 $r$ are kept in contact as shown. An electric current $i$ is passed through the bars. Which one of the following is correct?
supporting img

1 Heat produced in bar

B C

is 4 times the heat produced in bar

A B

.

2 Potential difference across

A B

is 4 times that of across

B C

.

3 Electric field in both halves is equal.

4 Current density across

A B

is double that of cross

B C

.

Explanation:

Current flowing through both the bars is equal.
Now, the heat produced is given by
$H = I^{2} R t \Rightarrow H \propto R$
$\frac{H_{A B}}{H_{B C}} = \frac{R_{A B}}{R_{B C}} = \frac{{(1 / 2 r)}^{2}}{{(1 / r)}^{2}} = \frac{1}{4} (R \propto \frac{1}{r^{2}})$

PHXII03:CURRENT ELECTRICITY

357142 The supply voltage in a room is 120 $V$ . The resistance of the lead wires is $6 Ω$ . 60 $W$ bulb is already switched on. What is the decrease of voltage across the bulb when a 240 $W$ heater is switched on in parallel to the bulb?

1 13.3

V

2 Zero

3 2.9

V

4 10.4

V

Explanation:

The resistance of the bulb is
$R = \frac{120 \times 120}{60} = 240 Ω$
$R_{e q} = 240 + 6 = 246 Ω$
supporting img
$V_{1} = \frac{240}{246} \times 120 = 117.073 V$
After connecting the heater

$V_{2} = \frac{48}{54} \times 120 = 106.66 V$
$V_{1} - V_{2} = 10.04 V$

PHXII03:CURRENT ELECTRICITY

357143 Assertion :
The coil of a heater is cut into two equal halves and only one of them is used into heater. The heater will now require half the time to produce the same amount of heat.
Reason :
The heat produced is directly proportional to square of current.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The power (heat produced per unit time) in a heater is given by $P = V^{2} / R$ , where $V$ is the voltage and $R$ is the resistance. If the resistance is halved by using only one-half of the coil, the power is doubled $(P = V^{2} / (R / 2) = 2 V^{2} / R)$ . Since power is directly proportional to the square of the current $(P α I^{2})$ , using half of the coil will result in the same amount of heat being produced in half the time, as stated in the assertion. So correct option is (2).

PHXII03:CURRENT ELECTRICITY

357144 For ensuring dissipation of same energy in all three resistors $(R_{1}, R_{2}, R_{3})$ connected as shown in figure, their values must be related as
supporting img

1

R_{1} = R_{2} = R_{3}

2

R_{2} = R_{3}

and

R_{1} = 4 R_{2}

3

R_{2} = R_{3}

and

R_{1} = \frac{R_{2}}{4}

4

R_{1} = R_{2} + R_{3}

Explanation:

The voltage across $R_{2}$ and $R_{3}$ is same.
Therefore, for same energy loss according to $H = \frac{V^{2}}{R} t, R_{2}$ must be equal to $R_{3}$ .
$i . e .$ $R_{2} = R_{3}$
Again, the energy is same in all resistances.
$∴ i^{2} R_{1} t = i_{1}^{2} R_{2} t (1)$
and $i_{1} = \frac{R_{3}}{R_{2} + R_{3}} i = \frac{R_{3}}{R_{3} + R_{3}} i = \frac{1}{2} i (2)$
$[∵ R_{2} = R_{3}]$
Thus, $i^{2} R_{1} t = \frac{i^{2}}{4} R_{2} t$ [From Eqs. (1) and (2)]
$∴ R_{1} = \frac{R_{2}}{4}$
So, correct option is (3)

AIIMS - 2005

PHXII03:CURRENT ELECTRICITY

357145 Assertion :
KWhr is a commercial unit used for expressing consumed electric energy.
Reason :
Kilo-Watt hour is the unit of electric power.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$(k W h r)$ is a unit of electric energy. It is calculated by multiplying the power in kilowatts $(k W)$ by the time in hours. This unit is commonly used to measure and express the amount of electric energy consumed. So correct option is (3).

PHXII03:CURRENT ELECTRICITY

357141 Two bars of radius $r$ and 2 $r$ are kept in contact as shown. An electric current $i$ is passed through the bars. Which one of the following is correct?
supporting img

1 Heat produced in bar

B C

is 4 times the heat produced in bar

A B

.

2 Potential difference across

A B

is 4 times that of across

B C

.

3 Electric field in both halves is equal.

4 Current density across

A B

is double that of cross

B C

.

Explanation:

Current flowing through both the bars is equal.
Now, the heat produced is given by
$H = I^{2} R t \Rightarrow H \propto R$
$\frac{H_{A B}}{H_{B C}} = \frac{R_{A B}}{R_{B C}} = \frac{{(1 / 2 r)}^{2}}{{(1 / r)}^{2}} = \frac{1}{4} (R \propto \frac{1}{r^{2}})$

PHXII03:CURRENT ELECTRICITY

357142 The supply voltage in a room is 120 $V$ . The resistance of the lead wires is $6 Ω$ . 60 $W$ bulb is already switched on. What is the decrease of voltage across the bulb when a 240 $W$ heater is switched on in parallel to the bulb?

1 13.3

V

2 Zero

3 2.9

V

4 10.4

V

Explanation:

The resistance of the bulb is
$R = \frac{120 \times 120}{60} = 240 Ω$
$R_{e q} = 240 + 6 = 246 Ω$
supporting img
$V_{1} = \frac{240}{246} \times 120 = 117.073 V$
After connecting the heater

$V_{2} = \frac{48}{54} \times 120 = 106.66 V$
$V_{1} - V_{2} = 10.04 V$

PHXII03:CURRENT ELECTRICITY

357143 Assertion :
The coil of a heater is cut into two equal halves and only one of them is used into heater. The heater will now require half the time to produce the same amount of heat.
Reason :
The heat produced is directly proportional to square of current.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The power (heat produced per unit time) in a heater is given by $P = V^{2} / R$ , where $V$ is the voltage and $R$ is the resistance. If the resistance is halved by using only one-half of the coil, the power is doubled $(P = V^{2} / (R / 2) = 2 V^{2} / R)$ . Since power is directly proportional to the square of the current $(P α I^{2})$ , using half of the coil will result in the same amount of heat being produced in half the time, as stated in the assertion. So correct option is (2).

PHXII03:CURRENT ELECTRICITY

357144 For ensuring dissipation of same energy in all three resistors $(R_{1}, R_{2}, R_{3})$ connected as shown in figure, their values must be related as
supporting img

1

R_{1} = R_{2} = R_{3}

2

R_{2} = R_{3}

and

R_{1} = 4 R_{2}

3

R_{2} = R_{3}

and

R_{1} = \frac{R_{2}}{4}

4

R_{1} = R_{2} + R_{3}

Explanation:

The voltage across $R_{2}$ and $R_{3}$ is same.
Therefore, for same energy loss according to $H = \frac{V^{2}}{R} t, R_{2}$ must be equal to $R_{3}$ .
$i . e .$ $R_{2} = R_{3}$
Again, the energy is same in all resistances.
$∴ i^{2} R_{1} t = i_{1}^{2} R_{2} t (1)$
and $i_{1} = \frac{R_{3}}{R_{2} + R_{3}} i = \frac{R_{3}}{R_{3} + R_{3}} i = \frac{1}{2} i (2)$
$[∵ R_{2} = R_{3}]$
Thus, $i^{2} R_{1} t = \frac{i^{2}}{4} R_{2} t$ [From Eqs. (1) and (2)]
$∴ R_{1} = \frac{R_{2}}{4}$
So, correct option is (3)

AIIMS - 2005

PHXII03:CURRENT ELECTRICITY

357145 Assertion :
KWhr is a commercial unit used for expressing consumed electric energy.
Reason :
Kilo-Watt hour is the unit of electric power.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$(k W h r)$ is a unit of electric energy. It is calculated by multiplying the power in kilowatts $(k W)$ by the time in hours. This unit is commonly used to measure and express the amount of electric energy consumed. So correct option is (3).

PHXII03:CURRENT ELECTRICITY

357141 Two bars of radius $r$ and 2 $r$ are kept in contact as shown. An electric current $i$ is passed through the bars. Which one of the following is correct?
supporting img

1 Heat produced in bar

B C

is 4 times the heat produced in bar

A B

.

2 Potential difference across

A B

is 4 times that of across

B C

.

3 Electric field in both halves is equal.

4 Current density across

A B

is double that of cross

B C

.

Explanation:

Current flowing through both the bars is equal.
Now, the heat produced is given by
$H = I^{2} R t \Rightarrow H \propto R$
$\frac{H_{A B}}{H_{B C}} = \frac{R_{A B}}{R_{B C}} = \frac{{(1 / 2 r)}^{2}}{{(1 / r)}^{2}} = \frac{1}{4} (R \propto \frac{1}{r^{2}})$

PHXII03:CURRENT ELECTRICITY

357142 The supply voltage in a room is 120 $V$ . The resistance of the lead wires is $6 Ω$ . 60 $W$ bulb is already switched on. What is the decrease of voltage across the bulb when a 240 $W$ heater is switched on in parallel to the bulb?

1 13.3

V

2 Zero

3 2.9

V

4 10.4

V

Explanation:

The resistance of the bulb is
$R = \frac{120 \times 120}{60} = 240 Ω$
$R_{e q} = 240 + 6 = 246 Ω$
supporting img
$V_{1} = \frac{240}{246} \times 120 = 117.073 V$
After connecting the heater

$V_{2} = \frac{48}{54} \times 120 = 106.66 V$
$V_{1} - V_{2} = 10.04 V$

PHXII03:CURRENT ELECTRICITY

357143 Assertion :
The coil of a heater is cut into two equal halves and only one of them is used into heater. The heater will now require half the time to produce the same amount of heat.
Reason :
The heat produced is directly proportional to square of current.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The power (heat produced per unit time) in a heater is given by $P = V^{2} / R$ , where $V$ is the voltage and $R$ is the resistance. If the resistance is halved by using only one-half of the coil, the power is doubled $(P = V^{2} / (R / 2) = 2 V^{2} / R)$ . Since power is directly proportional to the square of the current $(P α I^{2})$ , using half of the coil will result in the same amount of heat being produced in half the time, as stated in the assertion. So correct option is (2).

PHXII03:CURRENT ELECTRICITY

357144 For ensuring dissipation of same energy in all three resistors $(R_{1}, R_{2}, R_{3})$ connected as shown in figure, their values must be related as
supporting img

1

R_{1} = R_{2} = R_{3}

2

R_{2} = R_{3}

and

R_{1} = 4 R_{2}

3

R_{2} = R_{3}

and

R_{1} = \frac{R_{2}}{4}

4

R_{1} = R_{2} + R_{3}

Explanation:

The voltage across $R_{2}$ and $R_{3}$ is same.
Therefore, for same energy loss according to $H = \frac{V^{2}}{R} t, R_{2}$ must be equal to $R_{3}$ .
$i . e .$ $R_{2} = R_{3}$
Again, the energy is same in all resistances.
$∴ i^{2} R_{1} t = i_{1}^{2} R_{2} t (1)$
and $i_{1} = \frac{R_{3}}{R_{2} + R_{3}} i = \frac{R_{3}}{R_{3} + R_{3}} i = \frac{1}{2} i (2)$
$[∵ R_{2} = R_{3}]$
Thus, $i^{2} R_{1} t = \frac{i^{2}}{4} R_{2} t$ [From Eqs. (1) and (2)]
$∴ R_{1} = \frac{R_{2}}{4}$
So, correct option is (3)

AIIMS - 2005

PHXII03:CURRENT ELECTRICITY

357145 Assertion :
KWhr is a commercial unit used for expressing consumed electric energy.
Reason :
Kilo-Watt hour is the unit of electric power.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$(k W h r)$ is a unit of electric energy. It is calculated by multiplying the power in kilowatts $(k W)$ by the time in hours. This unit is commonly used to measure and express the amount of electric energy consumed. So correct option is (3).

PHXII03:CURRENT ELECTRICITY

357141 Two bars of radius $r$ and 2 $r$ are kept in contact as shown. An electric current $i$ is passed through the bars. Which one of the following is correct?
supporting img

1 Heat produced in bar

B C

is 4 times the heat produced in bar

A B

.

2 Potential difference across

A B

is 4 times that of across

B C

.

3 Electric field in both halves is equal.

4 Current density across

A B

is double that of cross

B C

.

Explanation:

Current flowing through both the bars is equal.
Now, the heat produced is given by
$H = I^{2} R t \Rightarrow H \propto R$
$\frac{H_{A B}}{H_{B C}} = \frac{R_{A B}}{R_{B C}} = \frac{{(1 / 2 r)}^{2}}{{(1 / r)}^{2}} = \frac{1}{4} (R \propto \frac{1}{r^{2}})$

PHXII03:CURRENT ELECTRICITY

357142 The supply voltage in a room is 120 $V$ . The resistance of the lead wires is $6 Ω$ . 60 $W$ bulb is already switched on. What is the decrease of voltage across the bulb when a 240 $W$ heater is switched on in parallel to the bulb?

1 13.3

V

2 Zero

3 2.9

V

4 10.4

V

Explanation:

The resistance of the bulb is
$R = \frac{120 \times 120}{60} = 240 Ω$
$R_{e q} = 240 + 6 = 246 Ω$
supporting img
$V_{1} = \frac{240}{246} \times 120 = 117.073 V$
After connecting the heater

$V_{2} = \frac{48}{54} \times 120 = 106.66 V$
$V_{1} - V_{2} = 10.04 V$

PHXII03:CURRENT ELECTRICITY

357143 Assertion :
The coil of a heater is cut into two equal halves and only one of them is used into heater. The heater will now require half the time to produce the same amount of heat.
Reason :
The heat produced is directly proportional to square of current.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

The power (heat produced per unit time) in a heater is given by $P = V^{2} / R$ , where $V$ is the voltage and $R$ is the resistance. If the resistance is halved by using only one-half of the coil, the power is doubled $(P = V^{2} / (R / 2) = 2 V^{2} / R)$ . Since power is directly proportional to the square of the current $(P α I^{2})$ , using half of the coil will result in the same amount of heat being produced in half the time, as stated in the assertion. So correct option is (2).

PHXII03:CURRENT ELECTRICITY

357144 For ensuring dissipation of same energy in all three resistors $(R_{1}, R_{2}, R_{3})$ connected as shown in figure, their values must be related as
supporting img

1

R_{1} = R_{2} = R_{3}

2

R_{2} = R_{3}

and

R_{1} = 4 R_{2}

3

R_{2} = R_{3}

and

R_{1} = \frac{R_{2}}{4}

4

R_{1} = R_{2} + R_{3}

Explanation:

The voltage across $R_{2}$ and $R_{3}$ is same.
Therefore, for same energy loss according to $H = \frac{V^{2}}{R} t, R_{2}$ must be equal to $R_{3}$ .
$i . e .$ $R_{2} = R_{3}$
Again, the energy is same in all resistances.
$∴ i^{2} R_{1} t = i_{1}^{2} R_{2} t (1)$
and $i_{1} = \frac{R_{3}}{R_{2} + R_{3}} i = \frac{R_{3}}{R_{3} + R_{3}} i = \frac{1}{2} i (2)$
$[∵ R_{2} = R_{3}]$
Thus, $i^{2} R_{1} t = \frac{i^{2}}{4} R_{2} t$ [From Eqs. (1) and (2)]
$∴ R_{1} = \frac{R_{2}}{4}$
So, correct option is (3)

AIIMS - 2005

PHXII03:CURRENT ELECTRICITY

357145 Assertion :
KWhr is a commercial unit used for expressing consumed electric energy.
Reason :
Kilo-Watt hour is the unit of electric power.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$(k W h r)$ is a unit of electric energy. It is calculated by multiplying the power in kilowatts $(k W)$ by the time in hours. This unit is commonly used to measure and express the amount of electric energy consumed. So correct option is (3).

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