Question

An element with emf $\epsilon$ and internal resistance r is connected across an external resistance R. The maximum power is external circuit is 9 W. The current flowing through the circuit in these conditions is 3 A. Then which of the following is/are correct?

• A. $\epsilon =6V$
• B. $r=R$
• C. $r=1\Omega$
• D. $r=3\Omega$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $\epsilon =6V$
B $r=R$
C $r=1\Omega$

Current through the circuit $I=\frac{ϵ}{(r+R)}$
Power dissipated in external resistance is
$P=I^{2}R=\frac{{ϵ}^2}{(r+R{)}^2}R$
We know that power dissipated is maximum when r = R
$P_{max}=\frac{{ϵ}^{2}r}{(2r{)}^2}=\frac{{ϵ}^2}{4r}=9W,i=\frac{ϵ}{2r}=3A$
Solve to get , $ϵ=6Vandr=1\Omega$