356209
In an \(A.C.\) circuit, the instantaneous values of \(e.m.f.\) and current are \(E = 200\sin 314\,t\,volts\)and \(I=\sin (314 t+\pi / 3)\) ampere then the average power consumed in watts is
1 200
2 100
3 0
4 50
Explanation:
\(P_{\text {org }}=I_{r m s} V_{r m s} \cos \phi\) \(\Rightarrow P_{\text {avg }}=\langle P\rangle=\dfrac{1}{\sqrt{2}} \times \dfrac{200}{\sqrt{2}} \cos 60^{\circ}\) \( = 50\;W\). So, correct option is (4).
PHXII07:ALTERNATING CURRENT
356210
The average power dissipated in \(AC\) circuit is 2 Watt. If a current flowing through a circuit is 2\(A\) and impedance is \(1\Omega \), what is the power factor of the \(AC\) circuit ?
1 \(0\)
2 \(0.5\)
3 \(\frac{1}{{\sqrt 2 }}\)
4 \(1\)
Explanation:
Average power dissipated in \(A.C\). circuit is \(P = VI\cos \phi = {I^2}Z\cos \phi \) where \(\cos \phi \) is the power factor of the circuit. \( \Rightarrow \cos \phi = \frac{P}{{{I^2}Z}}\) Here,\(P = 2W,I = 2A,Z = 1\Omega \) \(\therefore \,\cos \phi = \frac{2}{{{{(2)}^2}(1)}} = \frac{1}{2} = 0.5\)
KCET - 2014
PHXII07:ALTERNATING CURRENT
356211
Statement A : The power in an ac circuit is minimum if the circuit has only a resistor. Statement B : Power of a circuit is independent of the phase angle.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
Explanation:
Power in a series ac circuit consisting of \(L\), \(C\) and \(R\) is given by \(P = {I_{rms}}{V_{rms}}\cos \phi \) where \(\phi = {\tan ^{ - 1}}\left( {\frac{{\left| {{X_L} - {X_C}} \right|}}{R}} \right)\) For a purely resistive circuit \({X_L} = 0\,\,\,{\mathop{\rm and}\nolimits} \,\,\,{X_C} = 0\,\) .Therefore \(\tan \phi = 0\,\,{\rm{or}}\,\,\phi = 0\) and thereby \(\cos \phi = 1\). The power is maximum as \(\cos \,\phi \) is maximum. Power depends on the phase angle through the power factor \(\cos \,\phi \). So option (4) is correct.
PHXII07:ALTERNATING CURRENT
356212
If the power factor changes from \(\frac{1}{2}\) to \(\frac{1}{4}\) keeping resistance unchanged then what is the increase in impedance in \(AC\)?
356209
In an \(A.C.\) circuit, the instantaneous values of \(e.m.f.\) and current are \(E = 200\sin 314\,t\,volts\)and \(I=\sin (314 t+\pi / 3)\) ampere then the average power consumed in watts is
1 200
2 100
3 0
4 50
Explanation:
\(P_{\text {org }}=I_{r m s} V_{r m s} \cos \phi\) \(\Rightarrow P_{\text {avg }}=\langle P\rangle=\dfrac{1}{\sqrt{2}} \times \dfrac{200}{\sqrt{2}} \cos 60^{\circ}\) \( = 50\;W\). So, correct option is (4).
PHXII07:ALTERNATING CURRENT
356210
The average power dissipated in \(AC\) circuit is 2 Watt. If a current flowing through a circuit is 2\(A\) and impedance is \(1\Omega \), what is the power factor of the \(AC\) circuit ?
1 \(0\)
2 \(0.5\)
3 \(\frac{1}{{\sqrt 2 }}\)
4 \(1\)
Explanation:
Average power dissipated in \(A.C\). circuit is \(P = VI\cos \phi = {I^2}Z\cos \phi \) where \(\cos \phi \) is the power factor of the circuit. \( \Rightarrow \cos \phi = \frac{P}{{{I^2}Z}}\) Here,\(P = 2W,I = 2A,Z = 1\Omega \) \(\therefore \,\cos \phi = \frac{2}{{{{(2)}^2}(1)}} = \frac{1}{2} = 0.5\)
KCET - 2014
PHXII07:ALTERNATING CURRENT
356211
Statement A : The power in an ac circuit is minimum if the circuit has only a resistor. Statement B : Power of a circuit is independent of the phase angle.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
Explanation:
Power in a series ac circuit consisting of \(L\), \(C\) and \(R\) is given by \(P = {I_{rms}}{V_{rms}}\cos \phi \) where \(\phi = {\tan ^{ - 1}}\left( {\frac{{\left| {{X_L} - {X_C}} \right|}}{R}} \right)\) For a purely resistive circuit \({X_L} = 0\,\,\,{\mathop{\rm and}\nolimits} \,\,\,{X_C} = 0\,\) .Therefore \(\tan \phi = 0\,\,{\rm{or}}\,\,\phi = 0\) and thereby \(\cos \phi = 1\). The power is maximum as \(\cos \,\phi \) is maximum. Power depends on the phase angle through the power factor \(\cos \,\phi \). So option (4) is correct.
PHXII07:ALTERNATING CURRENT
356212
If the power factor changes from \(\frac{1}{2}\) to \(\frac{1}{4}\) keeping resistance unchanged then what is the increase in impedance in \(AC\)?
356209
In an \(A.C.\) circuit, the instantaneous values of \(e.m.f.\) and current are \(E = 200\sin 314\,t\,volts\)and \(I=\sin (314 t+\pi / 3)\) ampere then the average power consumed in watts is
1 200
2 100
3 0
4 50
Explanation:
\(P_{\text {org }}=I_{r m s} V_{r m s} \cos \phi\) \(\Rightarrow P_{\text {avg }}=\langle P\rangle=\dfrac{1}{\sqrt{2}} \times \dfrac{200}{\sqrt{2}} \cos 60^{\circ}\) \( = 50\;W\). So, correct option is (4).
PHXII07:ALTERNATING CURRENT
356210
The average power dissipated in \(AC\) circuit is 2 Watt. If a current flowing through a circuit is 2\(A\) and impedance is \(1\Omega \), what is the power factor of the \(AC\) circuit ?
1 \(0\)
2 \(0.5\)
3 \(\frac{1}{{\sqrt 2 }}\)
4 \(1\)
Explanation:
Average power dissipated in \(A.C\). circuit is \(P = VI\cos \phi = {I^2}Z\cos \phi \) where \(\cos \phi \) is the power factor of the circuit. \( \Rightarrow \cos \phi = \frac{P}{{{I^2}Z}}\) Here,\(P = 2W,I = 2A,Z = 1\Omega \) \(\therefore \,\cos \phi = \frac{2}{{{{(2)}^2}(1)}} = \frac{1}{2} = 0.5\)
KCET - 2014
PHXII07:ALTERNATING CURRENT
356211
Statement A : The power in an ac circuit is minimum if the circuit has only a resistor. Statement B : Power of a circuit is independent of the phase angle.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
Explanation:
Power in a series ac circuit consisting of \(L\), \(C\) and \(R\) is given by \(P = {I_{rms}}{V_{rms}}\cos \phi \) where \(\phi = {\tan ^{ - 1}}\left( {\frac{{\left| {{X_L} - {X_C}} \right|}}{R}} \right)\) For a purely resistive circuit \({X_L} = 0\,\,\,{\mathop{\rm and}\nolimits} \,\,\,{X_C} = 0\,\) .Therefore \(\tan \phi = 0\,\,{\rm{or}}\,\,\phi = 0\) and thereby \(\cos \phi = 1\). The power is maximum as \(\cos \,\phi \) is maximum. Power depends on the phase angle through the power factor \(\cos \,\phi \). So option (4) is correct.
PHXII07:ALTERNATING CURRENT
356212
If the power factor changes from \(\frac{1}{2}\) to \(\frac{1}{4}\) keeping resistance unchanged then what is the increase in impedance in \(AC\)?
NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXII07:ALTERNATING CURRENT
356209
In an \(A.C.\) circuit, the instantaneous values of \(e.m.f.\) and current are \(E = 200\sin 314\,t\,volts\)and \(I=\sin (314 t+\pi / 3)\) ampere then the average power consumed in watts is
1 200
2 100
3 0
4 50
Explanation:
\(P_{\text {org }}=I_{r m s} V_{r m s} \cos \phi\) \(\Rightarrow P_{\text {avg }}=\langle P\rangle=\dfrac{1}{\sqrt{2}} \times \dfrac{200}{\sqrt{2}} \cos 60^{\circ}\) \( = 50\;W\). So, correct option is (4).
PHXII07:ALTERNATING CURRENT
356210
The average power dissipated in \(AC\) circuit is 2 Watt. If a current flowing through a circuit is 2\(A\) and impedance is \(1\Omega \), what is the power factor of the \(AC\) circuit ?
1 \(0\)
2 \(0.5\)
3 \(\frac{1}{{\sqrt 2 }}\)
4 \(1\)
Explanation:
Average power dissipated in \(A.C\). circuit is \(P = VI\cos \phi = {I^2}Z\cos \phi \) where \(\cos \phi \) is the power factor of the circuit. \( \Rightarrow \cos \phi = \frac{P}{{{I^2}Z}}\) Here,\(P = 2W,I = 2A,Z = 1\Omega \) \(\therefore \,\cos \phi = \frac{2}{{{{(2)}^2}(1)}} = \frac{1}{2} = 0.5\)
KCET - 2014
PHXII07:ALTERNATING CURRENT
356211
Statement A : The power in an ac circuit is minimum if the circuit has only a resistor. Statement B : Power of a circuit is independent of the phase angle.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
Explanation:
Power in a series ac circuit consisting of \(L\), \(C\) and \(R\) is given by \(P = {I_{rms}}{V_{rms}}\cos \phi \) where \(\phi = {\tan ^{ - 1}}\left( {\frac{{\left| {{X_L} - {X_C}} \right|}}{R}} \right)\) For a purely resistive circuit \({X_L} = 0\,\,\,{\mathop{\rm and}\nolimits} \,\,\,{X_C} = 0\,\) .Therefore \(\tan \phi = 0\,\,{\rm{or}}\,\,\phi = 0\) and thereby \(\cos \phi = 1\). The power is maximum as \(\cos \,\phi \) is maximum. Power depends on the phase angle through the power factor \(\cos \,\phi \). So option (4) is correct.
PHXII07:ALTERNATING CURRENT
356212
If the power factor changes from \(\frac{1}{2}\) to \(\frac{1}{4}\) keeping resistance unchanged then what is the increase in impedance in \(AC\)?
