Physics Class 12 NCERT Solutions: Chapter 7 Alternating Current Part 5

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Phase angle in LCR circuit

Phase Angle in LCR Circuit

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Q: 13. A coil of inductance and resistance is connected to a, ac supply.

(A) What is the maximum current in the coil?

(B) What is the time lag between the voltage maximum and the current maximum?

Answer:

Inductance of the inductor,

Resistance of the resistor,

Potential of the supply voltage,

Frequency of the supply,

(A) Peak voltage is given as:

Angular frequency of the supply,

Maximum current in the circuit is given as:

(B) Equation for voltage is given as:

Equation for current is given as:

Where,

Phase difference between voltage and current

At time.

For,

Hence, the time lag between maximum voltage and maximum current is. Now, phase angle is given by the relation,

Hence, the time lag between maximum voltage and maximum current is.

Q: 14. Obtain the answers (A) to (B) Exercise 13 if the circuit is connected to a high frequency supply. Hence, explain the statement that at very high frequency, an inductor in a circuit nearly amounts to an open circuit. How does an inductor behave in a dc circuit after the steady state?

Answer:

Inductance of the inductor,

Resistance of the resistor,

Potential of the supply voltages,

Frequency of the supply,

Angular frequency,

(A) Peak voltage,

Maximum current,

(B) For phase difference, we have the relation:

It can be observed that is very small in this case. Hence, at high frequencies, the inductor amounts to an open circuit.

In a dc circuit, after a steady state is achieved. Hence, inductor L behaves like a pure conducting object.