A current i 1 = i 0 sin ωt passes through a resistor of resistance R. How much thermal energy is produced in one-time period? A current i 2 = – i 0 sin ωt passes through the resistor. How much thermal energy is produced in one-time period? If i 1 and i 2 both pass through the resistor simultaneously, how much thermal energy is produced? Is the principle of superposition obeyed in this case?

Question

Philoid · Accepted Answer

Same thermal energy, principle of superposition is obeyed.

Given:

Current

Formula used:

The thermal energy produced in one time period due to a current i is given by … (i), where i_rms = rms value of current, R = resistance, ω = angular frequency of oscillation of current

Now, the rms current i_rms in both cases is given by , where i₀ is the peak current.

Therefore, for current i₁, thermal energy produced is

and that produced for current i₂ is also where i₀ = peak value of current, R = resistance, ω = angular frequency of oscillation

Hence, the same thermal energy is produced due to both the currents individually. (Ans)

Since i₁ and i₂ have peak values i₀ and -i₀, they are equal and opposite in value. Hence, the net current through the resistor will be 0 when both pass through the resistor simultaneously. In this case, the thermal energy produced will be 0. (Ans)

Yes, the principle of superposition is obeyed in this case. (Ans)