# Numerical Problems : Alternating Current-II

#### LEVEL – II

Q:1. When 100 Volt D.C. is applied across a coil, a current of one ampere flows through it, when 100 V ac of 50 Hz is applied to the same coil, only 0.5 amp flows. Calculate the resistance and inductance of the coil.

Ans: 100 Ω , (√3/π) Hz

Q:2. A 50 W, 100 V lamp is to be connected to an ac mains of 200 V, 50 Hz. What capacitance is essential to be put in series with the lamp.

Ans: 9.2 μF

Q:3. A 10μF capacitor, an inductor and a resistor of 100 Ω are connected to an alternating source of emf 200 as shown in the figure. What is the r.m.s current in the circuit and the value of the inductance if the current and the source voltage attain their maxima simultaneously? What is the average power consumed in this case? Ans: 2 A , 10 H , 400 W

Q:4. A 200 Km long telegraph wire has capacity of 0.014μF /km. If it carries an alternating current of 50 KHz, what should be the value of an inductance required to be connected in series so that impedance is minimum ?

Ans: 0.303 H

Q:5. A coil of negligible resistance is connected in series with 90 Ω resistor across a 120 V – 60 Hz line. A voltmeter reads 36V across the resistance. Find the voltage across the coil and inductance of the coil.

Ans: 114 V , 0.76 H

Q:6. An ac source of angular frequency ω is fed across resistor R and a capacitor C is series. The current registered is I. If now the frequency of source is changed to ( but maintaining the same voltage), the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency ω.

Ans: $\displaystyle \sqrt{\frac{3}{5}}$

Q:7. An alternating current of 1.5mA and angular frequency ω = 300 rad/s flows through 10 KΩ resistor and a 0.50μF capacitor in series. Find the r.m.s. voltage across the capacitor and impedance of the circuit?

Ans: 10 V, 1.2 × 104 Ω

Q:8. A 750 Hz, 20 V source is connected to a resistance of 100 Ω, an inductance of 0.1803 H and a capacitance of 10 μF all in series. Calculate the time in which the resistance (thermal capacity 2 J/°C) will get heated by 10°C. (Ignore radiation)

Ans: 5.8 min

Q:9. In the circuit shown there is a box and capacitance C connected to alternating power source of angular frequency of 2 rad/s. Box has power factor and circuit has overall power factor 1. Find the impedance of the box. Ans: $\displaystyle \frac{1}{C \sqrt{2}}$ ohm

Q:10. In the given circuit, power factor between A and B is 0.5 and over all power factor of the circuit is 1. Find the value of R and L. Ans: 100 ohm , 5 H

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