Question

In an ac circuit, V and I are given by \[V=150\sin \left( 150t \right)V\,and\,I=\]

\[150\sin \left( 150t+\dfrac{\pi }{3} \right)A\].

The power dissipated in the circuit is

A. 106 W

B. 150 W

C. 5625 W

D. zero

Answer 1

Hint: Electric power is the rate, per unit time, at which electrical energy is dissipated by an electric circuit. The SI unit of the power is the watt, one joule for every second.

Complete answer:

Electric power is normally delivered by electric generators, however can likewise be provided by sources, for example, electric batteries. It is typically provided to organizations and homes (as household mains electricity) by the electric power industry through an electric power framework..

\[V\text{ }=\text{ }150\text{ }sin\text{ }\left( 150\text{ }t \right)V={{V}_{0}}sin\omega t,\text{ }we\text{ }get~{{V}_{0}}=\text{ }150\text{ }V\]

\[I=150\sin \left( 150+\dfrac{\pi }{3} \right)\]

\[I={{I}_{0}}sin(\omega t+\phi )\]

\[{{I}_{0}}=150A,\phi =\dfrac{\pi }{3}=60\]

\[P=\dfrac{1}{2}{{V}_{0}}{{I}_{0}}cos\phi =\dfrac{1}{2}150\times 150\times cos60\]

\[=\dfrac{1}{2}\times 150\times 150\times \dfrac{1}{2}=5625W\]

Therefore the correct option is C.

Electric power can be conveyed over long separations by transmission lines and utilized for applications, for example, motion, light or heat with high efficiency

Note: The power dissipated in an ac circuit depends on the power factor of the circuit. If the phase difference between the voltage and current is 90 degree, then the power factor of the circuit is zero and the power dissipated will also be zero.