Solved Numerical Problem No. 16.3 ( Unit-16: Alternating Current); HSSC-II (Class-12); Physics (Punjab Curriculum and Text Board, Lahore) With Verified Answers

Find the value of the current and inductive reactance when A.C. voltage of 220 V at 50 H z is passed through an inductor of 10 H. (Ans: $I_{rms}$ = 0.07 A, $X_L$ = 3140 Ω )

Data Given:

Voltage = V = 220 V

Frequency of A.C. supply = f = 50 Hz

Inductance = L = 10 H

To Find:

(i) Inductive Reactance =

$\X_L$ = ?

(ii) Root Mean Square (rms) current =

$\I_{rms}$ = ?

Solution:

(i) Inductive Reactance =

$\X_L$ = ?

The formula for inductive Reactance is given by:

$\X_L$ = ധL = 2ㄫfL

by putting values

$\X_L$ = ယ L = 2ㄫf L

by putting values

$\X_L$ = 2 ｘ 3.1416 ｘ 50 Hz ｘ 10 H

$\X_L$ = 3141.6 Ω ---------------Ans. 1

(ii) Root Mean Square (rms) current =

$\I_{rms}$ = ?

The current is given by:

$\I_{rms}$ =

$\frac {V}{X_L}$

$\I_{rms}$ =

$\frac {220 V}{3141.6 Ω}$

$\I_{rms}$ = 0.07 A -----------------------Ans. (2)

A coil having a resistance of 7 Ω and an inductance of 31.8 mH is connected to 230V, 50Hz supply. Calculate (a) the circuit current (b) phase angle (c) power factor. (d) power consumed. Ans (18.85, 55° lag, .573° lag, 2484.24 w)

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