A cell supplies a current of 2A when it is connected to a $5 Ω$ resistance and supplies current of 1.2A, if it is connected to a resistance of $9 Ω$ . Find the e.m.f of the cell.

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12V

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16V

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Solution

The correct option is C
12V

Given, $I_{1} = 2 A w h e n R_{1} = 5 Ω$
From relation $ϵ = I (R + r)$
$ϵ = 2 (5 + r) \dots \dots (i)$
Now, $I_{2} = 1.2 A w h e n R_{2} = 9 Ω$
$∴ ϵ = 1.2 (9 + r) \dots \dots (i i)$
From eqns. (i) and (ii)
$2 (5 + r) = 1.2 (9 + r)$
or, $10 + 2 r = 10.8 + 1.2 r$
or, $0.8 r = 0.8$
or, $r = \frac{0.8}{0.8} = 1 Ω$
Put the value of r in eqn. (i)
$ϵ = 2 (5 + 1) = 12 V$
$∴ ϵ = 12 V$

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A cell supplies a current of 2A when it is connected to a 5Ω resistance and supplies current of 1.2A, if it is connected to a resistance of 9Ω. Find the e.m.f of the cell.

The correct option is C 12V Given, I1=2A whenR1=5Ω From relation ϵ=I(R+r) ϵ=2(5+r)……(i) Now, I2=1.2A whenR2=9Ω ∴ϵ=1.2(9+r)……(ii) From eqns. (i) and (ii) 2(5+r)=1.2(9+r) or, 10+2r=10.8+1.2r or, 0.8r=0.8 or, r=0.80.8=1Ω Put the value of r in eqn. (i) ϵ=2(5+1)=12V ∴ϵ=12V

A cell supplies a current of 2A when it is connected to a $5 Ω$ resistance and supplies current of 1.2A, if it is connected to a resistance of $9 Ω$ . Find the e.m.f of the cell.