Current Electricity

JEE Main level, numerical answer, medium

310 of 380

Question 310 of 380

A moving coil of galvanometer when shunted with 2 Ω2\,\Omega resistance gives a full scale deflection for a current of 500500 mA. When a resistance of 470 Ω470\,\Omega is connected in series it gives a full scale deflection for 1010 V potential applied on it. The value of resistance of galvanometer coil is __________ Ω\Omega.

Show answer and solution

Answer: 50

Let GG be the resistance of the galvanometer and IgI_g be the current required for full scale deflection.

When the galvanometer is shunted with S=2 ΩS = 2\,\Omega, it acts as an ammeter of range I=500 mA=0.5 AI = 500\text{ mA} = 0.5\text{ A}. The potential difference across the galvanometer and the shunt is equal:

IgG=(I−Ig)SI_g G = (I - I_g) S

IgG=(0.5−Ig)×2I_g G = (0.5 - I_g) \times 2

IgG+2Ig=1I_g G + 2 I_g = 1

Ig=1G+2I_g = \dfrac{1}{G + 2}

When a resistance R=470 ΩR = 470\,\Omega is connected in series, it acts as a voltmeter of range V=10 VV = 10\text{ V}. The total voltage is the sum of the voltage drops:

V=Ig(G+R)V = I_g (G + R)

10=Ig(G+470)10 = I_g (G + 470)

Ig=10G+470I_g = \dfrac{10}{G + 470}

Equating the two expressions for IgI_g:

1G+2=10G+470\dfrac{1}{G + 2} = \dfrac{10}{G + 470}

G+470=10(G+2)G + 470 = 10(G + 2)

G+470=10G+20G + 470 = 10G + 20

9G=4509G = 450

G=50 ΩG = 50\,\Omega

Answer: 5050

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Circuit builder simulationDrag the sliders and watch the numbers in this question change.Revise Current Electricity firstFormula sheet, solved examples and the traps students fall into.

More Physics practice

JEE Main Physics practice question on Current Electricity (Electric Instruments), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.