Question

A certain network consists of two ideal and indentical voltage sources in series and a large number of ideal resistor. The power consumed in one of the resistor is $4W$ when either of the two sources is active and other is replaced by a short circuit. The power consumed by same resistor when both sources are simultaneously active would be:

• A. $0$ or $16W$
• B. $4W$ or $8W$
• C. $0$ or $8W$
• D. $8W$ or $16W$

Answer 1

The correct option is A $0$ or $16W$

$P=VI$

$I=\frac{nE}{R+r}$ (r=0)

In this case

$I=\frac{nE}{NR};E_1=E_2$

$P=VI$

In first case

$4=E\times \frac{E}{NR}=\frac{E^2}{NR}$

In second case

$x=2E\times \frac{2E}{NR}=\frac{4E^2}{NR}$

$\frac{x}{4}=\frac{4E^2}{NR}\times \frac{NR}{E^2}$

$x=0or16W$