An alternating voltage source of root-mean-square (RMS) voltage 200\ \text{V} is connected… — JAMB UTME

An alternating voltage source of root-mean-square (RMS) voltage $200\ \text{V}$ is connected across a series combination of a resistor with resistance $60\ \Omega$ and a capacitor with capacitive reactance $80\ \Omega$ . Calculate the root-mean-square current in the circuit.

Answer: 2 A

Answer

The root-mean-square current flowing through the circuit is 2 A.

The total impedance of the series RC circuit is obtained via quadrature sum

Z = \sqrt{R^2 + X_C^2} = \sqrt{60^2 + 80^2} = 100\ \Omega

. Dividing the RMS supply voltage (

200\ \text{V}

) by this impedance gives an RMS current of

2\ \text{A}

Step-by-Step Solution

Calculate the total impedance of the series RC circuit.

Z = \sqrt{R^2 + X_C^2} = \sqrt{60^2 + 80^2} = \sqrt{3600 + 6400} = 100\ \Omega

In an AC circuit with resistance and capacitive reactance in series, the total Opposition (impedance) is found by phasor addition.

Apply Ohm's law for alternating current circuits to find RMS current.

I_{\text{rms}} = \frac{V_{\text{rms}}}{Z} = \frac{200\ \text{V}}{100\ \Omega} = 2\ \text{A}

The RMS current is equal to the RMS voltage divided by the total circuit impedance.

Key Concept

Impedance and RMS Current in AC Series Circuits

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