Question

the output emf of a generator is given by v (t) = a sin(ω t), where a = 130 v. find the rms current in the circuit when this generator is connected to a 81.4 ω resistor. answer in units of a.\

Answer 1

To calculate the RMS current in a circuit with a generator connected to a resistor, one must divide the RMS voltage by the resistance. In this case, the RMS current is 1.13 A.

Step-by-step explanation:

The student is asking how to calculate the RMS current in a circuit consisting of a generator connected to a resistor. The output EMF of the generator is V(t) = a sin(ωt), with a peak voltage (amplitude) a of 130 V. To find the RMS current, we use the formula for the RMS (Root Mean Square) voltage, which is VRMS = VMAX / √2. For a resistor R of 81.4 Ω, Ohm's Law gives us the RMS current IRMS = VRMS / R.

First, compute the RMS voltage: VRMS = 130 V / √2 = 91.92 V.

Next, calculate the RMS current: IRMS = 91.92 V / 81.4 Ω = 1.13 A.

Therefore, the RMS current in the circuit is 1.13 A.