Question

The voltage across the circuit in the figure and the current through it, are given by the following expressions:

V(t) = 5 - 10 cos$(\omega t+{60}^0)$ V

i(t) = 5 +X cos $\left(\omega t\right)$ A

Where, $\omega$ = 100$\pi$ radian/s. If the average power delivered to the circuit is zero, then the value of X(in ampere) is (upto 2 decimal places).

Answer 1

Given that,

V(t) = 5 - 10 cos$(\omega t+{60}^0)$

i(t) = 5 + X cos $(\omega t+0^0)$

$P_{req}$ = 0

0 = 5 x 5 + $\frac{1}{2}$ $\left[\right(-10\left)\right(X\left)cos\right({60}^0\left)\right]$

X = 10