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Standard XII

Physics

Charging of Capacitors

Under what co...

Question

Under what conditions current passing through a resistance $R$ can 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.

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Solution

From the given diagram, we observe that both cells are in series combination with same polarity. So,

Equivalent emf, $E_{e q} = E_{1} + E_{2}$

And equivalent resistance of the circuit will be

$R_{e q} = R + r_{1} + r_{2}$

The current through the circuit before the battery of emf $E_{2}$ is short-circuited is,

$I_{1} = \frac{E_{e q}}{R_{e q}} = \frac{E_{1} + E_{2}}{R + r_{1} + r_{2}}$

After short-circuiting the battery of emf $E_{2}$ , current through resistance $R$ would be,

$I_{2} = \frac{E_{1}}{R + r_{1}}$

Now, $I_{2} > I_{1}$

$∴ \frac{E_{1}}{R + r_{1}} > \frac{E_{1} + E_{2}}{R + r_{1} + r_{2}}$

$\Rightarrow E_{1} r_{2} > E_{2} (R + r_{1})$

Hence, the correct answer is option $(b)$ .

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Q. Two unequal resistances, R1 and R2, are connected across two batteries of emf ε1 and ε2 internal resistance r1 and r2. Can the thermal energies developed in R1 and R2 be equal in a given time if current is same in each circuit? If yes, what will be the condition?

Q. A battery of emf E and internal resistance r sends current I1 and I2, when connected to external resistance R1 and R2 respectively. Determine the emf and internal resistance of the battery.

Q. The emf (V) and internal resistance (

r

) of a single battery which is equivalent to a parallel combination of two batteries of emf's

V_{1}

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(IIT-JEE 1997)

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Charging of Capacitors

Standard XII Physics

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Under what conditions current passing through a resistance R can be increased by short-circuiting the battery of emf E2. The internal resistances of the two batteries are r1 and r2 respectively.

Under what conditions current passing through a resistance $R$ can 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.