Question

A capacitor of 25 μF, inductor of 0.1 H and resistor of resistance 25 Ω are connected in series with an A.C. source of e.m.f. e = 310 sin (314 t) volt . What is the (i) reactance ? (ii) impedance and the current of the circuit ? (iii) phase angle between current and applied e.m.f. ? (iv) expression for instantaneous value of current ?

Answer 1

Explanation:

Given ω=314⇒2πf=314⇒f=50Hz

Total reactance of the circuit is a combination of capacitive and inductive reatance which is given by

∣X

C

−X

L

∣=∣

ω

C

1

−ωL∣=∣

314×25×10

−6

1

−314×0.1∣

=96Ω

Impendance of the circuit is

Z=

R

2

+(X

C

−X

L

)

2

=

25

2

+96

2

=99.2Ω

We have to find rms current in hte circuit in the current. It is given by

I

v

=

Z

E

v

=

99.2

310

2

=2.21A

Let ϕ be the angle by which current lead emf, then

tan(ϕ)=

R

X

C

−X

L

=

25

96

⇒ϕ=75.4

o

=1.31red