A circuit has three elements, a resistance of 11Ω , a coil of inductive reactance 120Ω and a capacitive reactance of 120Ω in series and connected to an A.C. source of 110 V , 60 Hz . Which of the thre

Question

A circuit has three elements, a resistance of 11Ω , a coil of inductive reactance 120Ω and a capacitive reactance of 120Ω in series and connected to an A.C. source of 110 V , 60 Hz . Which of the three elements have minimum potential difference?

TestHub · Accepted Answer

The circuit is an RLC series circuit.

Given:

Resistance $R = 11Ω$

Inductive reactance $X_{L} = 120Ω$

Capacitive reactance $X_{C} = 120Ω$

Source voltage $V = 110 V$

Since $X_{L} = X_{C}$ , the circuit is in resonance.

At resonance, the impedance $Z = R$ .

The current in the circuit is $I = \frac{V}{Z} = \frac{V}{R} = \frac{110 V}{11Ω} = 10 A$ .

The potential differences across each element are:

Potential difference across resistance: $V_{R} = I \times R = 10 A \times 11Ω = 110 V$

Potential difference across inductor: $V_{L} = I \times X_{L} = 10 A \times 120Ω = 1200 V$

Potential difference across capacitor: $V_{C} = I \times X_{C} = 10 A \times 120Ω = 1200 V$

Comparing the potential differences: $V_{R} = 110 V$ , $V_{L} = 1200 V$ , $V_{C} = 1200 V$ .

The resistance has the minimum potential difference.

The final answer is $R es i s t an ce$ .

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