Question

In the circuit shown in the figure the ac source gives a voltage $V = 20\cos(2000t)$. Neglecting source resistance, the

voltmeter and ammeter reading will be

• A. $0V,0.47A$
• B. $1.68V,0.47A$
• C. $0V,1.4A$
• D. $5.6V,1.4A$

Answer 1

Answer: (D)

$5.6V,1.4A$

Answer 2

$X_{L} = \omega L$ = 2000 × 5 × 10^–3 = 10 Ω and

$X_{C} = \frac{1}{2000 \times 50 \times 10^{- 6}} = 10\Omega$

Total impedance of the circuit

$= 6 + \sqrt{(R)^{2} + (X_{L} - X_{C})^{2}} = 6 + \sqrt{(4)^{2} + 0} = 10\Omega$Ammeter reads r.m.s. current so it's value $i_{rms} = \frac{V_{rms}}{\text{Total impedance}} = \frac{20/\sqrt{2}}{10} = \sqrt{2} = 1.41A$Since X_L = X_C ; this is the condition of resonance and in this condition V = V_R = iR = 1.4 × 4 = 5.6 V.