Question

Voltage input in a circuit is \[V = 300\sin (\omega t)\] with current \[I = 100\cos (\omega t)\]. Average power loss in the circuit is
A. \[3000\] units
B. \[1500\] units
C. \[1000\] units
D. Zero.

Answer 1

Hint: To solve this question, we have to know what is impedance. This is an effective resistance of any electric circuit to a.c. current, which arises from the combination of Ohmic resistance and reactance.

Complete step by step answer:
Here we know that, \[100\cos (\omega t) = 100\sin (\omega t - \pi /2)\].We can say from this equation that the current phase is shifted \[\pi /2\] radians from the voltage. So, we can say, the voltage and the current as magnitude and phase :
\[V = 300 < 0\]
\[\Rightarrow I = 100 < \pi /2\]
Now, after solving the impedance equation, we can write,
\[V = IZ\] here we know that V is equal to voltage, I is equal to current and Z is equal to the impedance.
So now, for Z,
\[Z = V/I\]
$\Rightarrow Z = 100 < \pi \dfrac{{300 < 0}}{{100 < \pi /2}} \\
\therefore Z = 3 < - \dfrac{\pi }{2} $
This equation means that the impedance is an ideal three Farad capacitor.So, we can say, a purely reactive impedance consumes no power, because it returns all of the energy on the negative part of the cycle ,that was introduced on the positive part of the cycle.

So the right answer will be option D.

Note: We can get confused between impedance, resistance and reactance. But these are different from each other. Impedance is the combined effect of resistance and reactance. But many times we use resistance as impedance where there is no reactance, only resistance is present. Reactance is also like resistance but it does not lead to dissipation of electrical energy as heat.