Ncert Exercises & Solutions

For an \(LCR\) circuit, the power transferred from the driving source to the driven oscillator is \(P = I^2Z\cos\phi\).

(a)	Here, the power factor \(\cos\phi \ge0, ~P \ge0.\)
(b)	The driving force can give no energy to the oscillator \((P=0)\) in some cases.
(c)	The driving force cannot syphon out \((P<0)\) the energy out of the oscillator.
(d)	The driving force can take away energy out of the oscillator.

Choose the correct options:
1. (a), (b), (c)
2. (a), (c), (d)
3. (b), (c), (d)
4. (c), (d)

(1) Hint: The power factor depends on the impedance of the circuit.

Step 1: According to the question power transferred,

P = I^{2} Z \cos φ

Where I is the current, Z = Impedance and cos

φ

is the power factor.

As power factor,

cosφ = \frac{R}{Z}

Where

R > 0 and Z > 0

\Rightarrow cosφ > 0 \Rightarrow P > 0