Question

A resistor and a capacitor are connected in series to a 50 Hz ac source. The rms voltage across the resistor and capacitor are 151 V and 160.3 V respectively. Calculate the rms voltage of the source. Also find the capacitive reactance and impedance of the circuit, if the current in the circuit is 0.755 A.

Answer 1

Answer:

The RMS voltage of the source is 220.22 volt

Impedance of circuit is 291.68 ohm

The capacitive reactance is 212.3 ohm  

Explanation:

Given as :

A resistor and a capacitor are connected in series to a 50 Hz ac source.

The rms voltage across the resistor = $V_r$ = 151 volt

The rms voltage across the capacitor = $V_c$ = 160.3 volt

Let The RMS voltage of the source = V volt

According to question

V = $\sqrt{v_r^{2}+v_c^{2} }$

i.e V = $\sqrt{151^{2}+160.3^{2} }$

Or, V = √48497.09

∴  V = 220.22

So, The RMS voltage of the source = V = 220.22 volt

Again'

Current = $\dfrac{source voltage}{impedance}$

i.e 0.755 = $\dfrac{220.22}{X}$

∴   X = $\dfrac{220.22}{0.755}$

i.e Impedance of circuit = X = 291.68   ohm

Since the circuit is in series

So, Current through capacitive reactance = $x_c$ = $\dfrac{v_c}{I}$

i.e  

Or, $x_c$ = $\dfrac{160.3}{0.755}$

So, The capacitive reactance = 212.3 ohm

Hence, The RMS voltage of the source is 220.22 volt

            Impedance of circuit is 291.68 ohm

            The capacitive reactance is 212.3 ohm  Answer