Ncert Exercises & Solutions

Study the circuits (a) and (b) shown in the figure and answer the following questions.

(a) Under which conditions would the RMS currents in the two circuits be the same?

(b) Can the RMS current in the circuit (b) be larger than that in (a)?

Hint: The currents in the circuits depends on the impedance of the circuit.

Step 1: Let,

{(I_{rms})}_{a} = rms current in circuit (a)

{(I_{rms})}_{b} = rms current in circuit (b)

{(I_{rms})}_{a} = \frac{V_{rms}}{R} = \frac{V}{R}

{(I_{rms})}_{b} = \frac{V_{rms}}{Z} = \frac{V}{\sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}}

(a) Stp 2: When,

{(I_{rms})}_{a} = {(I_{rms})}_{b}

R = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}

X_{L} = X_{C}, resonance condition

(b) Step 3: As

Z \geq R

\Rightarrow \frac{{(I_{rms})}_{a}}{{(I_{rms})}_{b}} = \frac{\sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}}{R}

= \frac{Z}{R} \geq 1

\Rightarrow {(I_{rms})}_{a} \geq {(I_{rms})}_{b}

No, the arms current in the circuit (b), cannot be larger than that in (a)