Question

In an a.c. circuit V and I are given by $V=100\sin (100t)volts$ and $I=100\sin (100t+\dfrac{\pi }{3})mA$. The power dissipated in the
circuit is
(A) $10^{4}watt$
(B) 10 watt
(C) 2.5 watt
(D) 5.0 watt

Answer 1

Hint
Power dissipation is the process by which an electronic device produces heat as an undesirable derivative of its primary action. The average ac power is found by multiplying the rms values of current and voltage. In an ac circuit, there is a phase angle between the source voltage and the current. The average power delivered to an RLC circuit is affected by the phase angle.

Complete step by step answer
General equation for voltage is given by: $V= V_{0}\sin (\omega t)$ … (1)
General equation for current is given by\textbf{ : } $I= I_{0}\sin (\omega t+\varphi )$ … (2)
Given equations are
$\Rightarrow V=100\sin (100t)volts$ … (3)
$\Rightarrow I=100\sin (100t+\dfrac{\pi }{3})mA$ … (4)
On comparing 1 and 2 with 3 and 4 respectively we get
$\Rightarrow V_{0}$ = 100; I=100mA; $\varphi =\dfrac{\pi }{3}$
Now we will calculate $I_{rms}$ and $V_{rms}$
$\Rightarrow I_{rms}=\dfrac{I_{o}}{\sqrt{2}}$
Substituting the value,
$\Rightarrow \dfrac{100\times 10^{-3}}{\sqrt{2}}$
$V_{rms}=\dfrac{V}{\sqrt{2}}$
Substituting the value,
$\Rightarrow \dfrac{100}{\sqrt{2}}$
Formula for power dissipation is given by:
$\Rightarrow P=I_{rms}\times V_{rms}\times \cos (\varphi )$
After putting the value in the equation we get,
$\Rightarrow P=\dfrac{100\times 10^{-3}}{\sqrt{2}}\times \dfrac{100}{\sqrt{2}}\times \cos (\dfrac{\pi }{3})$
P = 2.5 watt
Hence, Correct option is (C).

Note
The circuit that's excited using an alternating source is named an AC Circuit. The AC is employed for domestic and industrial purposes. In an AC circuit, the worth of the magnitude and therefore the direction of current and voltages isn't constant, it changes at a daily interval of your time. The magnitude of three phase ac circuit power is three times more than the power of the single-phase circuit. The power factor determines the total useful power flows in the circuit. In AC Circuit, the current and voltages are represented by magnitude and direction.