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JEE Main 20149 AprilOnline

Exam: JEE Main
Year: 2014
Date: 9 April
Mode: Online
Subject: Physics
Chapter: Alternating Current

JEE Main 2014 · 9 April · Online · Physics · Alternating Current

When the rms voltages V _ L , V _ C and V _ R are measured...

When the rms voltages

{V}_{L} , {V}_{C}

and

{V}_{R}

are measured respectively across the inductor

L,

the capacitor

C

and the resistor

R

in a series

LCR

circuit connected to an

AC

source, it is found that the ratio

{V}_{L} : {V}_{C} : {V}_{R} = 1: 2: 3.

If the rms voltage of the

AC

source is

100V,

then

{V}_{R}

is close to : When the rms voltages V _ L , V _ C and V _ R are measured respectively across the inductor L, the capacitor C and the

When the rms voltages V _ L , V _ C and V _ R are measured respectively across the inductor L, the capacitor C and the

When the rms voltages V _ L , V _ C and V _ R are measured respectively across the inductor L, the capacitor C and the

When the rms voltages V _ L , V _ C and V _ R are measured respectively across the inductor L, the capacitor C and the

Options

A $50V$
B $70V$
C $100V$
D $90V$

Correct answer

D. $90V$

Step-by-step solution

{V}_{L} : {V}_{C} : {V}_{R} = 1: 2: 3

{V}_{\text{rms}} = 100\text{V}

then

{V}_{R} = ?

When the rms voltages V _ L , V _ C and V _ R are measured respectively across the inductor L, the capacitor C and the

Let

{V}_{L} = x,

then

{V}_{C} = 2x

and

{V}_{R} = 3x

using

V = \sqrt{{V}_{R}^{2} + {( {V}_{c} - {V}_{L} )}^{2}}

1 0 0 = \sqrt{{\left(3 x\right)}^{2} + {\left(2 x - x\right)}^{2}}

1 0 0 = \sqrt{1 0 {x}^{2}}

When the rms voltages V _ L , V _ C and V _ R are measured respectively across the inductor L, the capacitor C and the

When the rms voltages V _ L , V _ C and V _ R are measured respectively across the inductor L, the capacitor C and the

x = \dfrac{1 0 0}{\sqrt{1 0}}

= 10\sqrt{10}

∴ {V}_{R} = 3 x

= 30\sqrt{10} \approx 90V

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