Question

In above shown figure, a circuit has resistor R and battery of emf $\epsilon$. If current I is flowing through circuit then power dissipated as heat is P. The circuit is changed by doubling the emf $\epsilon$ of the battery while R is kept constant. After the change, the power dissipated in R is:

• A. $\frac{P}{4}$
• B. $\frac{P}{2}$
• C. $P$
• D. $2P$
• E. $4P$

Answer 1

The correct option is E $4P$

Given - resistance in circuit $R_1=R$ , emf ${\epsilon }_1=\epsilon$ and power $P_1=P$

power of circuit

$P={\epsilon }^2/R$ ...........$.eq\left(1\right)$

when emf is doubled and resistance is kept constant

$R_2=R$ , ${\epsilon }_2=2\epsilon$ , $P_2=?$

$P_2=\left(\right(2\epsilon {)}^2)/R$..............$eq\left(2\right)$

dividing $eq\left(2\right)$ by $eq\left(1\right)$

$P_2=4P$