Under what conditions can the current passing | vedclass

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

Question

(B) The current through the circuit before the battery of emf $E_2$ is short-circuited is given by:$I_1 = \frac{E_1 + E_2}{R + r_1 + r_2}$After short-

Vedclass · Accepted Answer

$E_1r_2 > E_2(R + r_1)$

Vedclass · Answer

(B) The current through the circuit before the battery of emf $E_2$ is short-circuited is given by:$I_1 = \frac{E_1 + E_2}{R + r_1 + r_2}$After short-circuiting the battery of emf $E_2$,the current through the resistance $R$ becomes:$I_2 = \frac{E_1}{R + r_1}$For the current to increase,we must have $I_2 > I_1$:$\frac{E_1}{R + r_1} > \frac{E_1 + E_2}{R + r_1 + r_2}$Cross-multiplying gives:$E_1(R + r_1 + r_2) > (E_1 + E_2)(R + r_1)$$E_1R + E_1r_1 + E_1r_2 > E_1R + E_1r_1 + E_2R + E_2r_1$Subtracting $E_1R + E_1r_1$ from both sides:$E_1r_2 > E_2(R + r_1)$

Under what conditions can the current passing through a resistance $R$ be increased by short-circuiting the battery of emf $E_2$? The internal resistances of the two batteries are $r_1$ and $r_2$ respectively.

Similar Questions

In the given circuit,what is the voltage between $P$ and $Q$ in $V$?

Two long coaxial and conducting cylinders of radius $a$ and $b$ are separated by a material of conductivity $\sigma$ and a constant potential difference $V$ is maintained between them by a battery. Then the current per unit length of the cylinder flowing from one cylinder to the other is -

The effective resistance between $A$ and $B$ of the shown network,where the resistance of each resistor is $R$,is

The potential difference across the terminals of the battery shown in the figure is ................. $V$. ($r$ = internal resistance of the battery)

If the ammeter in the given figure shows a reading of $2 \, A$,find the value of $R$ in $\Omega$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module