Question

A current i1 = i0 sin ωt passes through a resistor of resistance R. How much thermal energy is produced in one time period? A current i2 = −i0 sin ωt passes through the resistor. How much thermal energy is produced in one time period? If i1 and i2 both pass through the resistor simultaneously, how much thermal energy is produced? Is the principle of superposition obeyed in this case?

Answer 1

Explanation:

Steps 1:

• The generated thermal energy in a single time period for an AC circuit is given by,

$H=I_{r m s}^{2} \times R \times \frac{2 \pi}{\omega}$

• In case of current, $i_{1}=i_{0} \sin \omega t$,

$I_{r m s}=\frac{i_{0}}{\sqrt{2}}$  

$H=\frac{i_{0}^{2} \mathrm{R}}{2} \times \frac{2 \pi}{\omega}=\frac{\pi i_{0}^{2} \mathrm{R}}{w}$

Step 2:

• In case of  current, $i_{2}=-i_{0} \sin \omega t$,

$I_{r m s}=\frac{i_{0}}{\sqrt{2}}$

Step 3:

• Because of this current the same thermal energy will be generated.

• Because $i_{1}$ and $i_{2}$ are opposite in direction and the size is equivalent, When they both travel together, The total current via the resistor becomes zero. Indeed, for this case the concept of superposition is being obeyed.