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

$R > 0 and Z > 0$

$\Rightarrow cosφ > 0 \Rightarrow P > 0$