JEE Main 2016 · Physics · Work, Energy and Power · easy

A battery of internal resistance r delivers the same power to an external resistance of 2 Ω as to one of 8 Ω. The maximum power the battery can…

Single correct option

A battery of internal resistance

r

delivers the same power to an external resistance of

2\ \Omega

as to one of

8\ \Omega

. The maximum power the battery can deliver to any external resistor is

25\ \mathrm{W}

. The power it delivers to the

2\ \Omega

resistor is

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Answer: (C) $22.2\ \mathrm{W}$

Power in

R

P=\dfrac{E^2R}{(R+r)^2}

. Equal power for

R_1

and

R_2

requires

r^2=R_1R_2

, so

r=\sqrt{2\times8}=4\ \Omega

. The maximum power occurs when

R=r

and equals

\dfrac{E^2}{4r}=25

, giving

E^2=400

and

E=20\ \mathrm{V}

. Then for the

2\ \Omega

resistor the current is

\dfrac{20}{2+4}=\dfrac{10}{3}\ \mathrm{A}

and

P=\left(\dfrac{10}{3}\right)^2\times2=\dfrac{200}{9}\approx22.2\ \mathrm{W}

. The same value is obtained for

8\ \Omega

\left(\dfrac{20}{12}\right)^2\times8=22.2\ \mathrm{W}

, confirming the choice

r=4\ \Omega

Original question written in the JEE Main 2016 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake