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**Introductory Exercise 25.1**

**Ques 1: An electric lamp which runs at 100 V dc and consumes 10 A current is connected to ac mains at 150 V, 50 Hz cycles with a choke coil in series. Calculate the inductance and drop of voltage across the choke. Neglect the resistance of choke.Sol:**

= 0.036 H

Sol:

**Introductory Exercise 25.2**

**Ques 1: If a 0.03 H inductor, a 10Î© resistor and a 2Î¼F capacitor are connected in series. At what frequency will they resonate? What will be the phase angle at resonance?Sol:**

Sol:

= 0.2

**ExercisesFor JEE Main**

**Subjective QuestionsQues 1: (a) What is the reactance of a 2.00 H inductor at a frequency of 50.0 Hz? (b) What is the inductance of an inductor whose reactance is 2.00Î© at 50.0 Hz? (c) What is the reactance of a 2.00 Î¼F capacitor at a frequency of 50.0 Hz? (d) What is the capacitance of a capacitor whose reactance is 2.00Î© at 50.0 Hz?**

(b) Since X

(c) (V

(V

(V

(a) What is the power factor?

(b) What is the average power delivered by the source?

(c) The capacitor is replaced by one wit h C = 0.0360 Î¼B and the source frequency is adjusted to the new resonance value. Then, what is the average power delivered by the source?

Sol:

(a) What circuit element, an inductor or a capacitor, should be placed in series with the circuit to raise its power factor?

(b) What size element will raise the power factor to unit y?

Sol:

X

Power factor,

To increase the power factor denominator should decrease.

Hence X

R = 0.72 Z = 0.72 Ã— 60 = 43.2 Î©

New inductor of inductance 41.64 Î© should be added in the circuit.

V(t) = 170sin (6280 t +Ï€/3) volt

i(t) = 8.5sin(6280t + Ï€/2)amp

(a) Plot the two waveforms.

(b) Determine the frequency in Hz.

(c) Determine the power factor stating its nature.

(d) What are the values of the elements?

Sol:

Power factor = cos Î¦ = cos 30Â°

= âˆš3/2

From the given functions of V and i we can see that current function leads the voltage function.

...(i)

âˆ´

= 10 Î©

= 15.92 Ã— 10

(a) 100 rad/s (b) 1000 rad/s (c) 10000 rad/s

Sol:

(a) Derive an expression for the circuit current.

(b) Determine the inductive reactance of the inductor.

(c) Derive an expression for the voltage V

Sol:

= 8.33 mA

Current function and V

I = (8.33 mA) cos [(950 rad/s) t]

(b) X

(c) (V

= 6.33V

Now, V

F

(a) What are the phase angle and power factor for this circuit?

(b) What is the impedance of the circuit?

(c) What is the rms voltage of the source?

(d) What average power is delivered by the source?

(e) What is the average rate at which electrical energy is converted to thermal energy in the resistor?

(f) What is the average rate at which electrical energy is dissipated ( converted to other forms) in the capacitor?

(g) In the inductor?

Sol:

= 343Î©

= 45.6Â°

= 240/343

= 0.699

Since X

(b) Impedance = Z = 343Î©

(c) V

= 0.45 Ã— 343 = 155 V

= (0.45)

(e) P = P

(f) P

(g) P

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