A battery supplies 150 W and 196 W power to two resistors of 6 Ω and 4 Ω when they are connected separately to it. The internal resistance of the battery is

Question

A battery supplies 150 W and 196 W power to two resistors of 6 Ω and 4 Ω when they are connected separately to it. The internal resistance of the battery is (A) 2 Ω (B) 2.5 Ω (C) 0.5 Ω (D) 1 Ω

Tardigrade Admin · Accepted Answer

P propto (R/(R + r)2) ∴ (P1/P2) = (R1 /R2) ((R2 + r)2/(R1 + r)2) i.e. (150/196) = (6/4) ((4 + r)2/4 ( 6 + r)2) i.e. r = 1 Ω

Q. A battery supplies 150 W and 196 W power to two resistors of $6 Ω$ and $4 Ω$ when they are connected separately to it. The internal resistance of the battery is

$2 Ω$

$2.5 Ω$

$0.5 Ω$

$1 Ω$

P $\propto \frac{R}{( R + r ) ^{2}}$
$∴$ $\frac{P _{1}}{P _{2}} = \frac{R _{1}}{R _{2}} \frac{( R _{2} + r ) ^{2}}{( R _{1} + r ) ^{2}}$
$i . e .$ $\frac{150}{196} = \frac{6}{4} \frac{( 4 + r ) ^{2}}{4 ( 6 + r ) ^{2}} i . e . r = 1Ω$

Q. A battery supplies 150 W and 196 W power to two resistors of 6Ω and 4Ω when they are connected separately to it. The internal resistance of the battery is

2Ω

2.5Ω

0.5Ω

1Ω