A resistor of 20Ω and a capacitor are connected in series with an AC current source of 50 Hz. What should be the capacitance to produce a phase…

Question

A resistor of 20Ω and a capacitor are connected in series with an AC current source of 50 Hz. What should be the capacitance to produce a phase difference of 30° between the voltage and current?

MARKS Content Team · Accepted Answer

Correct answer: (B) √32πmF. Capacitive reactance is given by, X_C=1/(ωC) ⇒X_C=1/(2×π×f×C) ⇒X_C=1/(2×π×50×C)=1/(100π×C) Impedance of the circuit is given by, Z=√(R^2+XC^2) ...1 Power factor is given by, cosϕ=R/Z ⇒cos30°=20/Z ⇒√32=20/Z ⇒Z=(40√3 ΩUsing equation 1, we have⇒√(R^2+XC^2)=40√3⇒R^2+XC^2=1600)/3 ⇒20^2+XC^2=1600/3 ⇒XC^2=1600/3-400=400/3 ⇒X_C=20√3 ⇒C=√320×100π ⇒C=√32π mF

A resistor of $20 Ω$ and a capacitor are connected in series with an $A C$ current source of $50 Hz .$ What should be the capacitance to produce a phase difference of $30 °$ between the voltage and current?

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