
Q1 A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply.
(a) What is the rms value of current in the circuit?
(b) What is the net power consumed over a full cycle?Ans: Resistance of the resistor, R = 100 Ω
Supply voltage, V = 220 V
Frequency, ν = 50 Hz
(a) The rms value of current in the circuit is given as:
I = V / R
= 220 / 100 = 2.20 A
(b) The net power consumed over a full cycle is given as:
P = VI
= 220 × 2.2 = 484 W
Q2 (a) The peak voltage of an ac supply is 300 V. What is the rms voltage?
(b) The rms value of current in an ac circuit is 10 A. What is the peak current?
Ans: (a) Peak voltage of the ac supply, V_{0} = 300 V
Rms voltage is given as:
(b) Therms value of current is given as:
I = 10 A
Now, peak current is given as:
Q3 A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.
Ans: Inductance of inductor, L = 44 mH = 44 × 10^{3} H
Supply voltage, V = 220V
Frequency, ν = 50Hz
Angular frequency, \[\begin{align}\omega = 2\pi v\end{align}\]
Inductive reactance, \begin{align}X_{L}= \omega L = 2\pi vL = 2\pi\times50\times44\times10^{3} \Omega\end{align}
Rms value of current is given as:
\begin{align}I = \frac{v}{X_{L}}\end{align}
\begin{align} = \frac{220}{2\pi\times50\times44\times 10^{3}} =15.92A\end{align}
Hence, the rms value of current in the circuit is 15.92 A.