A cell of internal resistance r drives current through an external resistance R. The power delivered by the cell to the external resistance will be maximum when

Question

A cell of internal resistance r drives current through an external resistance R. The power delivered by the cell to the external resistance will be maximum when (A) R = 1000 r (B) R = 0.001 r (C) R = 2r (D) R = r

Tardigrade Admin · Accepted Answer

Current i = (E/r + R) Power generated in R P = i2 R P = (E2R/(r + R)2) for maximum power (dP/dR) = 0 E2 [((r+R)2 ×1-R ×2(r+R)/(r+R)4)] = 0 ⇒ r =R

Q. A cell of internal resistance r drives current through an external resistance $R$ . The power delivered by the cell to the external resistance will be maximum when

R = 1000 r

R = 0.001 r

R = 2r

R = r

Current $i = \frac{E}{r + R}$
Power generated in R
$P = i^{2} R$
$P = \frac{E ^{2} R}{( r + R ) ^{2}}$
for maximum power $\frac{d P}{d R} = 0$
$E^{2} [\frac{( r + R ) ^{2} \times 1 - R \times 2 ( r + R )}{( r + R ) ^{4}}] = 0$
$\Rightarrow r = R$

Q. A cell of internal resistance r drives current through an external resistance R. The power delivered by the cell to the external resistance will be maximum when