Q13 of 31 Page 267

A coil of inductance 0.50 H and resistance 100 W is connected to a 240 V, 50 Hz A.C. supply.

(a) What is the maximum current in the coil?


(b) What is the time lag between the voltage maximum and the current maximum?

Given: Inductance = 0.50 H

Resistance R = 100 Ω


Voltage V = 240 V


Frequency = 50 Hz


The diagram is:



(a) Peak voltage is given by the following formula:


V0 = √2 V


V0 = √2 × 240V


On calculating, we get


V0 = 339.41 V


Angular frequency is given by the formula ω = 2πv


Substituting value of v in above formula


ω = 2 × π × 50(Hz) = 100 π rad/s.


The maximum current in the coil can be calculated as follows:




On calculating, we get


I0 = 1.82 A


(b) The equation for voltage and current are as follows:


V = V0 cos ωt


I = I0 cos (ωt-Ф)


At time t = 0, V = V0


At t = Ф/ ω, I = I0


Therefore, the time lag between maximum current and maximum voltage is Ф/ ω. Phase angle is given by the following relation:


tan Ф = ωL/R


tan Ф = (2 π × 50(Hz) × 0.5(H))/100


On calculating, we get


tan Ф = 1.57


or Ф = 57.50


in rad Ф = 57.5π/180 rad


ωt = 57.5π/180


or


On calculating, we get


t = 3.2 ms


More from this chapter

All 31 →
11

Figure 7.21 shows a series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, C = 80μF, R = 40Ω.


(a) Determine the source frequency which drives the circuit in resonance.


(b) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.


(c) Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.

 12

An LC circuit contains a 20 mH inductor and a 50 μF capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0.

(a) What is the total energy stored initially? Is it conserved during LC oscillations?


(b) What is the natural frequency of the circuit?


(c) At what time is the energy stored


(i) completely electrical (i.e., stored in the capacitor)? (ii) completely magnetic (i.e., stored in the inductor)?


(d) At what times is the total energy shared equally between the inductor and the capacitor?


(e) If a resistor is inserted in the circuit, how much energy is eventually dissipated as heat?

 14

Obtain the answers (a) to (b) in Exercise 13 if the circuit is connected to a high frequency supply (240 V, 10 kHz). Hence, explain the statement that at very high frequency, an inductor in a circuit nearly amounts to an open circuit. How does an inductor behave in a dc circuit after the steady state?

 15

A 100 μF capacitor in series with a 40Ω resistance is connected to a 110 V, 60 Hz supply.

(a) What is the maximum current in the circuit?


(b) What is the time lag between the current maximum and the voltage maximum?