When an A C source of voltage V=V0 sin 100 t is connected across a circuit, the phase difference between the voltage V and current I in the circuit is observed to be π / 4, as shown in figure. If the circuit consists possibly only of R C or R L or L C in series, find possible values of two elements.

Question

When an A C source of voltage V=V0 sin 100 t is connected across a circuit, the phase difference between the voltage V and current I in the circuit is observed to be π / 4, as shown in figure. If the circuit consists possibly only of R C or R L or L C in series, find possible values of two elements. (A) R=1 k Ω, C=10 μ F (B) R=1 k Ω, C=1 μ F (C) R=1 k Ω, L=10 m H (D) R=10 k Ω, L=10 m H

Tardigrade Admin · Accepted Answer

Figure given in the question shows that current

I

leads the voltage

V

by a phase angle

π /4

.
Therefore, the circuit can be

RC

circuit alone.

tan ϕ = \frac{X _{C}}{R} = \frac{1}{ω CR}

(∵ X_{C} = \frac{1}{ω C})

tan \frac{π}{4} = \frac{1}{ω CR}; 1 = \frac{1}{ω CR}

...(i)
From

V = V_{0} sin 100 t

,
we get,

ω = 100 r a d s^{- 1}

∴ CR = \frac{1}{ω} = \frac{1}{100}

(using (i))
When

R = 1 k Ω = 1 0^{3} Ω,

C = \frac{1}{1 0 ^{5}} = 1 0^{- 5} F = 10 μ F

$R = 1 k Ω, C = 10 μ F$

$R = 1 k Ω, C = 1 μ F$

$R = 1 k Ω, L = 10 m H$

$R = 10 k Ω, L = 10 m H$

Q. When an AC source of voltage V=V0​sin100t is connected across a circuit, the phase difference between the voltage V and current I in the circuit is observed to be π/4, as shown in figure. If the circuit consists possibly only of RC or RL or LC in series, find possible values of two elements.

R=1kΩ,C=10μF

R=1kΩ,C=1μF

R=1kΩ,L=10mH

R=10kΩ,L=10mH

$R = 1 k Ω, C = 10 μ F$

$R = 1 k Ω, C = 1 μ F$

$R = 1 k Ω, L = 10 m H$

$R = 10 k Ω, L = 10 m H$