Question

N cells each of emf E and identical resistance r are grouped into sets of K cells connected in series. The sets are connected in parallel to a load of resistance R, then

• A. Maximum power is delivered to the load if K = $\sqrt{\frac{NR}{r}}$
• B. Maximum power is delivered to the load if K = $\sqrt{\frac{r}{NR}}$
• C. Maximum power delivered to the load is $\frac{E^2}{4Nr}$
• D. Maximum power delivered to the load is $\frac{N{E}^2}{4r}$

Answer 1

Answer: (A), (D)

The correct options are
A

Maximum power is delivered to the load if K = $\sqrt{\frac{NR}{r}}$

D

Maximum power delivered to the load is $\frac{N{E}^2}{4r}$

Maximum power delivered when internal resistance = external resistance
$\Rightarrow \frac{Kr}{\left(\frac{N}{K}\right)}=RK=\sqrt{\frac{NR}{r}}$
Max power delivered $=I^{2}R$
$=\frac{(KE{)}^2}{{(\frac{K^{2}r}{N}+R)}^2}R=\frac{K^2{E}^2}{4R}=\frac{N{E}^2}{4r}$