Question

In an AC circuit $E = 220\sin (100\pi t)$ if the Impedance is $110\Omega $ and phase angle is $\phi = 60^\circ $ the power consumption is
A. $55W$
B. $110W$
C. $220W$
D. $440W$

Answer 1

Hint: In order to solve this question we need to understand peak value and root mean square value. Peak value of voltage or current is maximum voltage or current flow in alternating current circuit whereas Root mean Square value of voltage or current value is on an average value with which current or voltage flows in alternating current circuit. Impedance is the value of net resistance or opposition offered by a circuit against the flow of current. Phase angle is the angle with which voltage and current lag with each other.

Complete step by step answer:
Given value of voltage in alternating current circuit is, $E = 220\sin (100\pi t)$
Comparing with $E = {E_{\max }}\sin (\omega t)$
We get, ${E_{\max }} = 220V$
Also Impedance given, $Z = 110\Omega $
So Peak value of current is, ${I_{\max }} = \dfrac{{{E_{\max }}}}{Z}$
Putting values we get, ${I_{\max }} = \dfrac{{220}}{{110}}A$
${I_{\max }} = 2A$
Using formula for Power dissipation, $P = \dfrac{1}{2}({E_{\max }})({I_{\max }})\cos \phi $
Putting values we get,
$P = \dfrac{1}{2} \times (220) \times (2) \times \cos (60^\circ )$
$\Rightarrow P = 220 \times \dfrac{1}{2}$ Since $\cos (60^\circ ) = \dfrac{1}{2}$
$\therefore P = 110W$

The correct option is B.

Note: It should be remembered that alternating current is different from direct current, alternating current continuously varies with time and it repeats itself after periodic intervals whereas direct current is constant current applied across circuits. Alternating current is necessary for circuits having capacitors and inductors because with direct current capacitor once fully charged behave as open circuit and inductor once full charge behave as closed circuit so no variation and exchange of energy happens between inductor and capacitor. Whereas due to a current capacitor once fully charged quickly discharges and thereby creates a magnetic field around the inductor whereas when inductor gets fully charged it quickly discharges and thereby arranging charges on plates of capacitor, so in this exchange of energy happens.