Question

A 100 \(\Omega\) resistor is connected to a 220 V, 50 Hz supply.
Calculate:
(i) r.m.s. value of current
(ii) net power consumed over the full cycle

Hint:

To find the r.m.s. value of current in an AC circuit, divide the voltage by the resistance. The power consumed in a purely resistive circuit is proportional to the square of the current.

Answer 1

Step 1: r.m.s. value of current.
The r.m.s. value of current \( I_{\text{rms}} \) is given by the formula: \[ I_{\text{rms}} = \frac{V}{R} \] where \( V \) is the supply voltage and \( R \) is the resistance. Substituting the given values: \[ I_{\text{rms}} = \frac{220}{100} = 2.2 \, \text{A} \]
Step 2: Net power consumed.
The net power consumed by the resistor is given by: \[ P = V_{\text{rms}} \cdot I_{\text{rms}} = I_{\text{rms}}^2 \cdot R \] Substituting the value of \( I_{\text{rms}} \) and \( R \): \[ P = (2.2)^2 \cdot 100 = 4.84 \cdot 100 = 484 \, \text{W} \]
Step 3: Conclusion.
The r.m.s. value of current is \( 2.2 \, \text{A} \), and the net power consumed is \( 484 \, \text{W} \).