In a series LCR circuit the voltage across an inductor, capacitor and resistor are 20 V, 20 V and 40 V respectively. The phase difference between the applied voltage and the current in the circuit is

Question

In a series LCR circuit the voltage across an inductor, capacitor and resistor are 20 V, 20 V and 40 V respectively. The phase difference between the applied voltage and the current in the circuit is (A) 30° (B) 45° (C) 60° (D) 0°

Tardigrade Admin · Accepted Answer

Let (φ) be the phase difference between the applied voltage and current. Then tan φ=(XL-XC/R) =(IV(XL-XC)/IVR) =(VL-VC/VR) =(20 V-20 V/40 V) =0 ∴ φ =tan-1(0)=0°

Q. In a series $L CR$ circuit the voltage across an inductor, capacitor and resistor are $20 V$ , $20 V$ and $40 V$ respectively. The phase difference between the applied voltage and the current in the circuit is

$3 0^{°}$

$4 5^{°}$

$6 0^{°}$

$0^{°}$

Let $(ϕ)$ be the phase difference between the applied voltage and current. Then
$t an ϕ = \frac{X _{L} - X _{C}}{R}$
$= \frac{I _{V} ( X _{L} - X _{C} )}{I _{V} R}$
$= \frac{V _{L} - V _{C}}{V _{R}}$
$= \frac{20 V - 20 V}{40 V}$
$= 0$
$∴ ϕ = t a n^{- 1} (0) = 0^{\circ}$

Q. In a series LCR circuit the voltage across an inductor, capacitor and resistor are 20V, 20V and 40V respectively. The phase difference between the applied voltage and the current in the circuit is

30°

45°

60°

0°