07. Power in AC Circuit: the Power Factor
AC (NCERT)

274678 In an a.c. circuit $V$ and $I$ are given by
$\begin{array}{*{35}{r}}
{} & V=100\text{sin}\left( 100t \right)\text{ }\!\!~\!\!\text{ volts }\!\!~\!\!\text{ } \\
{} & \mathbf{I}=100\text{sin}\left( 100t+\pi /3 \right)\text{mA} \\
\end{array}$
the power dissipated in the circuit is

1 ${{10}^{4}}$ watt
2 10 watt
3 2.5watt
4 5.0 watt
AC (NCERT)

274679 The instantaneous values of alternating current and voltages in a circuit are given as
$\begin{array}{*{35}{r}}
{} & i=\frac{1}{\sqrt{2}}\text{sin}\left( 100\pi t \right)A \\
{} & e=\frac{1}{\sqrt{2}}\text{sin}\left( 100\pi t+\pi /3 \right)\text{ }\!\!~\!\!\text{ Volt }\!\!~\!\!\text{ } \\
\end{array}$
The average power in Watt consumed in the circuit is

1 $\frac{1}{4}$
2 $\frac{\sqrt{3}}{4}$
3 $\frac{1}{2}$
4 $\frac{1}{8}$
AC (NCERT)

274680 Two coils A and B are connected in series across a $240\text{V}$, $50\text{Hz}$ supply. The resistance of $\text{A}$ is $5\text{ }\!\!\Omega\!\!\text{ }$ and the inductance of $B$ is $0.02\text{H}$. The power consumed is $3\text{kW}$ and the power factor is 0.75 . The impedance of the circuit is

1 $0.144\text{ }\!\!\Omega\!\!\text{ }$
2 $1.44\text{ }\!\!\Omega\!\!\text{ }$
3 $14.4\text{ }\!\!\Omega\!\!\text{ }$
4 $144\text{ }\!\!\Omega\!\!\text{ }$
AC (NCERT)

274681 In an electrical circuit $R,L,C$ and an a.c. voltage source are all connected in series. When $L$ is removed from the circuit, the phase difference between the voltage the current in the circuit is $\pi /3$. If instead, $C$ is removed from the circuit, the phase difference is again $\pi /3$. The power factor of the circuit is

1 $1/2$
2 $1/\sqrt{2}$
3 1
4 $\sqrt{3}/2$
AC (NCERT)

274678 In an a.c. circuit $V$ and $I$ are given by
$\begin{array}{*{35}{r}}
{} & V=100\text{sin}\left( 100t \right)\text{ }\!\!~\!\!\text{ volts }\!\!~\!\!\text{ } \\
{} & \mathbf{I}=100\text{sin}\left( 100t+\pi /3 \right)\text{mA} \\
\end{array}$
the power dissipated in the circuit is

1 ${{10}^{4}}$ watt
2 10 watt
3 2.5watt
4 5.0 watt
AC (NCERT)

274679 The instantaneous values of alternating current and voltages in a circuit are given as
$\begin{array}{*{35}{r}}
{} & i=\frac{1}{\sqrt{2}}\text{sin}\left( 100\pi t \right)A \\
{} & e=\frac{1}{\sqrt{2}}\text{sin}\left( 100\pi t+\pi /3 \right)\text{ }\!\!~\!\!\text{ Volt }\!\!~\!\!\text{ } \\
\end{array}$
The average power in Watt consumed in the circuit is

1 $\frac{1}{4}$
2 $\frac{\sqrt{3}}{4}$
3 $\frac{1}{2}$
4 $\frac{1}{8}$
AC (NCERT)

274680 Two coils A and B are connected in series across a $240\text{V}$, $50\text{Hz}$ supply. The resistance of $\text{A}$ is $5\text{ }\!\!\Omega\!\!\text{ }$ and the inductance of $B$ is $0.02\text{H}$. The power consumed is $3\text{kW}$ and the power factor is 0.75 . The impedance of the circuit is

1 $0.144\text{ }\!\!\Omega\!\!\text{ }$
2 $1.44\text{ }\!\!\Omega\!\!\text{ }$
3 $14.4\text{ }\!\!\Omega\!\!\text{ }$
4 $144\text{ }\!\!\Omega\!\!\text{ }$
AC (NCERT)

274681 In an electrical circuit $R,L,C$ and an a.c. voltage source are all connected in series. When $L$ is removed from the circuit, the phase difference between the voltage the current in the circuit is $\pi /3$. If instead, $C$ is removed from the circuit, the phase difference is again $\pi /3$. The power factor of the circuit is

1 $1/2$
2 $1/\sqrt{2}$
3 1
4 $\sqrt{3}/2$
AC (NCERT)

274678 In an a.c. circuit $V$ and $I$ are given by
$\begin{array}{*{35}{r}}
{} & V=100\text{sin}\left( 100t \right)\text{ }\!\!~\!\!\text{ volts }\!\!~\!\!\text{ } \\
{} & \mathbf{I}=100\text{sin}\left( 100t+\pi /3 \right)\text{mA} \\
\end{array}$
the power dissipated in the circuit is

1 ${{10}^{4}}$ watt
2 10 watt
3 2.5watt
4 5.0 watt
AC (NCERT)

274679 The instantaneous values of alternating current and voltages in a circuit are given as
$\begin{array}{*{35}{r}}
{} & i=\frac{1}{\sqrt{2}}\text{sin}\left( 100\pi t \right)A \\
{} & e=\frac{1}{\sqrt{2}}\text{sin}\left( 100\pi t+\pi /3 \right)\text{ }\!\!~\!\!\text{ Volt }\!\!~\!\!\text{ } \\
\end{array}$
The average power in Watt consumed in the circuit is

1 $\frac{1}{4}$
2 $\frac{\sqrt{3}}{4}$
3 $\frac{1}{2}$
4 $\frac{1}{8}$
AC (NCERT)

274680 Two coils A and B are connected in series across a $240\text{V}$, $50\text{Hz}$ supply. The resistance of $\text{A}$ is $5\text{ }\!\!\Omega\!\!\text{ }$ and the inductance of $B$ is $0.02\text{H}$. The power consumed is $3\text{kW}$ and the power factor is 0.75 . The impedance of the circuit is

1 $0.144\text{ }\!\!\Omega\!\!\text{ }$
2 $1.44\text{ }\!\!\Omega\!\!\text{ }$
3 $14.4\text{ }\!\!\Omega\!\!\text{ }$
4 $144\text{ }\!\!\Omega\!\!\text{ }$
AC (NCERT)

274681 In an electrical circuit $R,L,C$ and an a.c. voltage source are all connected in series. When $L$ is removed from the circuit, the phase difference between the voltage the current in the circuit is $\pi /3$. If instead, $C$ is removed from the circuit, the phase difference is again $\pi /3$. The power factor of the circuit is

1 $1/2$
2 $1/\sqrt{2}$
3 1
4 $\sqrt{3}/2$
AC (NCERT)

274678 In an a.c. circuit $V$ and $I$ are given by
$\begin{array}{*{35}{r}}
{} & V=100\text{sin}\left( 100t \right)\text{ }\!\!~\!\!\text{ volts }\!\!~\!\!\text{ } \\
{} & \mathbf{I}=100\text{sin}\left( 100t+\pi /3 \right)\text{mA} \\
\end{array}$
the power dissipated in the circuit is

1 ${{10}^{4}}$ watt
2 10 watt
3 2.5watt
4 5.0 watt
AC (NCERT)

274679 The instantaneous values of alternating current and voltages in a circuit are given as
$\begin{array}{*{35}{r}}
{} & i=\frac{1}{\sqrt{2}}\text{sin}\left( 100\pi t \right)A \\
{} & e=\frac{1}{\sqrt{2}}\text{sin}\left( 100\pi t+\pi /3 \right)\text{ }\!\!~\!\!\text{ Volt }\!\!~\!\!\text{ } \\
\end{array}$
The average power in Watt consumed in the circuit is

1 $\frac{1}{4}$
2 $\frac{\sqrt{3}}{4}$
3 $\frac{1}{2}$
4 $\frac{1}{8}$
AC (NCERT)

274680 Two coils A and B are connected in series across a $240\text{V}$, $50\text{Hz}$ supply. The resistance of $\text{A}$ is $5\text{ }\!\!\Omega\!\!\text{ }$ and the inductance of $B$ is $0.02\text{H}$. The power consumed is $3\text{kW}$ and the power factor is 0.75 . The impedance of the circuit is

1 $0.144\text{ }\!\!\Omega\!\!\text{ }$
2 $1.44\text{ }\!\!\Omega\!\!\text{ }$
3 $14.4\text{ }\!\!\Omega\!\!\text{ }$
4 $144\text{ }\!\!\Omega\!\!\text{ }$
AC (NCERT)

274681 In an electrical circuit $R,L,C$ and an a.c. voltage source are all connected in series. When $L$ is removed from the circuit, the phase difference between the voltage the current in the circuit is $\pi /3$. If instead, $C$ is removed from the circuit, the phase difference is again $\pi /3$. The power factor of the circuit is

1 $1/2$
2 $1/\sqrt{2}$
3 1
4 $\sqrt{3}/2$