Question

When an ac generator of 120 V is connected in series with a capacitor and a resistor of 30 ohm, the circuit carries a current 1.5A. The potential difference across the capacitor will be
(a) 1.11 V
(b) 111 V
(c) Zero
(d) 220 V​

Answer 1

111 V

A capacitor is tantamount to a battery since it amasses electric charge when it interfaces with a power source. The capacitor has two close channels isolated by a cover (dielectric material), with one plate gathering a positive charge while the other fosters a negative charge. At the point when the need emerges, the capacitor will give the charge it has amassed to the generator. A capacitor has two essential capacities. Most importantly, it stores and deliveries an electric charge as per the current need. Furthermore, the capacitor is additionally liable for directing the voltage.

Answer 2

The potential difference across the capacitor will be about 111 V

Given:

• An ac generator of 120 V is connected in series with a capacitor and a resistor of 30 ohm,
• The circuit carries a current 1.5A.

To Find:

• The potential difference across the capacitor will be
• (a) 1.11 V
• (b) 111 V
• (c) Zero
• (d) 220 V​

Solution:

Step 1:

Find Voltage across Resistance

V = IR
V = 1.5 x 30

V = 45 V

Step 2:

Find Voltage across Capacitor

$(V_{total})^{2}=(V_{c})^2+(V_R)^2$

$(120)^{2}=(V_{c})^2+(45)^2$

$111.24 \approx (V_{c})$

Hence, from the given options 111V is the correct option

Correct option is b) 111 V

Another Method:

Z = V/I

Z =  120/1.5

Z = 80 Ω

$Z^2= R^2+(X_C)^2$

$(80)^2= (30)^2+(X_C)^2$    

$(80)^2= (30)^2+(X_C)^2$    

Xc ≈74.16

Vc = IXc

Vc = 1.5 x 74.16

Vc = 111.24 V

The potential difference across the capacitor will be about 111 V

Correct option is b) 111 V