QBManager

AC (NCERT)

274665 A.C. power is transmitted from a power house at a high voltage as

1 the rate of transmission is faster at high voltages

2 it is more economical due to less power loss

3 power cannot be transmitted at low voltages

4 a precaution against theft of transmission lines

NCERT Page-252 / N-191

AC (NCERT)

274666 An alternating voltage $V = V_{0} sin ω t$ is applied across a circuit. As a result, a current $I = I_{0} sin (ω t - π / 2)$ flows in it. The power consumed per cycle is

1 zero

2

0.5 V_{0} I_{0}

3

0.707 V_{0} I_{0}

4

1.414 V_{0} I_{0}

Explanation:

(a) The phase angle between voltage $V$ . and current $I$ is $π / 2$ . Therefore, power factor $cos ϕ = cos (π / 2) = 0$ . Hence the power consumed is zero.

NCERT Page-252 / N-191

AC (NCERT)

274667 The heat produced in a given resistance in a given time by the sinusoidal current $I_{0} sin ω t$ will be the same as that of a steady current of magnitude nearly

1

0.71 I_{0}

2

1.412 I_{0}

3

I_{0}

4

\sqrt{I_{0}}

NCERT Page-252/ N-191

AC (NCERT)

274668 An alternating e.m.f. of angular frequency $ω$ is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency

1

\frac{ω}{4}

2

\frac{ω}{2}

3

ω

4

2 ω

Explanation:

(d) Instantaneous values of emf and current in inductive circuit are given by $E = E_{0} sin ω t$ and $i = i_{0} sin (ω t - \frac{π}{2})$ respectively.
$∴ P_{inst} = E . i = E_{0} Sin ω t \times i_{0} Sin (ω t - \frac{π}{2})$
$= E_{0} i_{0} sin ω t (sin ω t cos \frac{π}{2} - cos ω t sin \frac{π}{2})$
$= - E_{0} i_{0} sin ω t cos ω t$
$= - \frac{1}{2} E_{0} i_{0} sin 2 ω t (sin 2 ω t = 2 sin ω tcos ω t)$
Hence, angular frequency of instantaneous power is $2 ω$

NCERT Page-252 / N-191

AC (NCERT)

274665 A.C. power is transmitted from a power house at a high voltage as

1 the rate of transmission is faster at high voltages

2 it is more economical due to less power loss

3 power cannot be transmitted at low voltages

4 a precaution against theft of transmission lines

NCERT Page-252 / N-191

AC (NCERT)

274666 An alternating voltage $V = V_{0} sin ω t$ is applied across a circuit. As a result, a current $I = I_{0} sin (ω t - π / 2)$ flows in it. The power consumed per cycle is

1 zero

2

0.5 V_{0} I_{0}

3

0.707 V_{0} I_{0}

4

1.414 V_{0} I_{0}

Explanation:

(a) The phase angle between voltage $V$ . and current $I$ is $π / 2$ . Therefore, power factor $cos ϕ = cos (π / 2) = 0$ . Hence the power consumed is zero.

NCERT Page-252 / N-191

AC (NCERT)

274667 The heat produced in a given resistance in a given time by the sinusoidal current $I_{0} sin ω t$ will be the same as that of a steady current of magnitude nearly

1

0.71 I_{0}

2

1.412 I_{0}

3

I_{0}

4

\sqrt{I_{0}}

NCERT Page-252/ N-191

AC (NCERT)

274668 An alternating e.m.f. of angular frequency $ω$ is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency

1

\frac{ω}{4}

2

\frac{ω}{2}

3

ω

4

2 ω

Explanation:

(d) Instantaneous values of emf and current in inductive circuit are given by $E = E_{0} sin ω t$ and $i = i_{0} sin (ω t - \frac{π}{2})$ respectively.
$∴ P_{inst} = E . i = E_{0} Sin ω t \times i_{0} Sin (ω t - \frac{π}{2})$
$= E_{0} i_{0} sin ω t (sin ω t cos \frac{π}{2} - cos ω t sin \frac{π}{2})$
$= - E_{0} i_{0} sin ω t cos ω t$
$= - \frac{1}{2} E_{0} i_{0} sin 2 ω t (sin 2 ω t = 2 sin ω tcos ω t)$
Hence, angular frequency of instantaneous power is $2 ω$

NCERT Page-252 / N-191

AC (NCERT)

274665 A.C. power is transmitted from a power house at a high voltage as

1 the rate of transmission is faster at high voltages

2 it is more economical due to less power loss

3 power cannot be transmitted at low voltages

4 a precaution against theft of transmission lines

NCERT Page-252 / N-191

AC (NCERT)

274666 An alternating voltage $V = V_{0} sin ω t$ is applied across a circuit. As a result, a current $I = I_{0} sin (ω t - π / 2)$ flows in it. The power consumed per cycle is

1 zero

2

0.5 V_{0} I_{0}

3

0.707 V_{0} I_{0}

4

1.414 V_{0} I_{0}

Explanation:

(a) The phase angle between voltage $V$ . and current $I$ is $π / 2$ . Therefore, power factor $cos ϕ = cos (π / 2) = 0$ . Hence the power consumed is zero.

NCERT Page-252 / N-191

AC (NCERT)

274667 The heat produced in a given resistance in a given time by the sinusoidal current $I_{0} sin ω t$ will be the same as that of a steady current of magnitude nearly

1

0.71 I_{0}

2

1.412 I_{0}

3

I_{0}

4

\sqrt{I_{0}}

NCERT Page-252/ N-191

AC (NCERT)

274668 An alternating e.m.f. of angular frequency $ω$ is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency

1

\frac{ω}{4}

2

\frac{ω}{2}

3

ω

4

2 ω

Explanation:

(d) Instantaneous values of emf and current in inductive circuit are given by $E = E_{0} sin ω t$ and $i = i_{0} sin (ω t - \frac{π}{2})$ respectively.
$∴ P_{inst} = E . i = E_{0} Sin ω t \times i_{0} Sin (ω t - \frac{π}{2})$
$= E_{0} i_{0} sin ω t (sin ω t cos \frac{π}{2} - cos ω t sin \frac{π}{2})$
$= - E_{0} i_{0} sin ω t cos ω t$
$= - \frac{1}{2} E_{0} i_{0} sin 2 ω t (sin 2 ω t = 2 sin ω tcos ω t)$
Hence, angular frequency of instantaneous power is $2 ω$

NCERT Page-252 / N-191

AC (NCERT)

274665 A.C. power is transmitted from a power house at a high voltage as

1 the rate of transmission is faster at high voltages

2 it is more economical due to less power loss

3 power cannot be transmitted at low voltages

4 a precaution against theft of transmission lines

NCERT Page-252 / N-191

AC (NCERT)

274666 An alternating voltage $V = V_{0} sin ω t$ is applied across a circuit. As a result, a current $I = I_{0} sin (ω t - π / 2)$ flows in it. The power consumed per cycle is

1 zero

2

0.5 V_{0} I_{0}

3

0.707 V_{0} I_{0}

4

1.414 V_{0} I_{0}

Explanation:

(a) The phase angle between voltage $V$ . and current $I$ is $π / 2$ . Therefore, power factor $cos ϕ = cos (π / 2) = 0$ . Hence the power consumed is zero.

NCERT Page-252 / N-191

AC (NCERT)

274667 The heat produced in a given resistance in a given time by the sinusoidal current $I_{0} sin ω t$ will be the same as that of a steady current of magnitude nearly

1

0.71 I_{0}

2

1.412 I_{0}

3

I_{0}

4

\sqrt{I_{0}}

NCERT Page-252/ N-191

AC (NCERT)

274668 An alternating e.m.f. of angular frequency $ω$ is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency

1

\frac{ω}{4}

2

\frac{ω}{2}

3

ω

4

2 ω

Explanation:

(d) Instantaneous values of emf and current in inductive circuit are given by $E = E_{0} sin ω t$ and $i = i_{0} sin (ω t - \frac{π}{2})$ respectively.
$∴ P_{inst} = E . i = E_{0} Sin ω t \times i_{0} Sin (ω t - \frac{π}{2})$
$= E_{0} i_{0} sin ω t (sin ω t cos \frac{π}{2} - cos ω t sin \frac{π}{2})$
$= - E_{0} i_{0} sin ω t cos ω t$
$= - \frac{1}{2} E_{0} i_{0} sin 2 ω t (sin 2 ω t = 2 sin ω tcos ω t)$
Hence, angular frequency of instantaneous power is $2 ω$

NCERT Page-252 / N-191

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