When two identical batteries of internal resi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the $EMF$ of each battery be $E$ and internal resistance be $r = 1 \Omega$.In series connection,total $EMF$ $= 2E$ and total internal resistan

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) Let the $EMF$ of each battery be $E$ and internal resistance be $r = 1 \Omega$.In series connection,total $EMF$ $= 2E$ and total internal resistance $= 2r = 2 \Omega$.The current $I_s = \frac{2E}{R + 2}$.The power $P_1 = I_s^2 R = \left(\frac{2E}{R + 2}\right)^2 R$.In parallel connection,total $EMF$ $= E$ and total internal resistance $= \frac{r}{2} = 0.5 \Omega$.The current $I_p = \frac{E}{R + 0.5}$.The power $P_2 = I_p^2 R = \left(\frac{E}{R + 0.5}\right)^2 R$.Given $P_1 = 2.25 P_2$,so $\left(\frac{2E}{R + 2}\right)^2 R = 2.25 \left(\frac{E}{R + 0.5}\right)^2 R$.Dividing both sides by $E^2 R$,we get $\frac{4}{(R + 2)^2} = 2.25 \frac{1}{(R + 0.5)^2}$.Taking square root on both sides: $\frac{2}{R + 2} = \frac{1.5}{R + 0.5}$.$2(R + 0.5) = 1.5(R + 2) \implies 2R + 1 = 1.5R + 3$.$0.5R = 2 \implies R = 4 \Omega$.

Similar Questions

Assertion : $A$ larger dry cell has higher $emf$.
Reason : The $emf$ of a dry cell is proportional to its size.

The value of the internal resistance of an ideal cell is:

Four identical cells,each having an electromotive force $(e.m.f.)$ of $12\,V$,are connected in parallel. The resultant electromotive force $(e.m.f.)$ of the combination is .............. $V$.

For a cell,the terminal potential difference $(P.D.)$ is $2.2\;V$ when the circuit is open and reduces to $1.8\;V$ when the cell is connected to an external resistance of $R = 5\;\Omega$. Determine the internal resistance $(r)$ of the cell.

Vedclass Test Series

Exam Paper Generator

Online Exam Module