Question

An AC generator with an output rms voltage of 18.0 V at a frequency of 60.0 Hz is connected across a 85.0-μF capacitor. Find the following. (a) capacitive reactance (b) rms current (c) maximum current in the circuit (d) Does the capacitor have its maximum charge when the current takes its maximum value? O Yes O No

Answer 1

Answer:

(A) 31.22 ohm (B) 0.5765 A (C)0.8152 A (D) yes

Explanation:

We have given voltage V =18 volt

Frequency f=60 Hz

Capacitance $C=85\mu F=80\times 10^{-6}F$

(A) Capacitive reactance $X_C=\frac{1}{\omega C}=\frac{1}{2\pi fC}=\frac{1}{2\times 3.14\times 60\times 85\times 10^{-6}}=31.22ohm$

(B) Rms current $i=\frac{V}{X_C}=\frac{18}{31.22}=0.5765A$

(C) Maximum current $i_m=\sqrt{2}i_{rms}=1.414\times 0.5765=0.8152A$

(D) We know that charge Q=current ×time , so from the relation we can see that if current will be maximum then charge will also be maximum