Exercise

EXERCISE

1. A coil of inductance 31.8 mH and resistance 10 Ω is connected in parallel with a capacitor across a 250V, 50Hz supply. Determine the value of capacitance if no reactive current is taken from supply.

Hint: The circuit is at resonance. Taking f₀ = 50Hz, find C.

[Ans: 159 μF]

2. Prove that the impedance of the circuit shown in the figure is equal to R and is therefore independent of frequency if R2 = . Find the value of the impedance for L = 0.02 H and C = 100 μF.

[Ans: 14.14 Ω]

3. An inductive circuit of resistance 202 and inductance 0.01H is connected to a 250V, 50Hz supply. What capacitance must be connected in parallel with this inductive circuit to produce resonance? Find the total current from the supply and the current in each branch.

 [Ans: 721 μF, 36.1A, 56.6A, 67.2A]

4. Determine the value of C in the network shown in the figure to yield resonance.

 [Ans: 24 mF]

5. A variable inductive reactance X_L is connected in parallel with a series combination of resistance R and capacitive reactance X_C. For resonance derive an expression for X_L in terms of R and X_C.

Ans : [R² +X_c² / X_c]