For two cells having the same EMF E and internal resistance r, the current passing through the external resistor is the same when both the cells are connected either in parallel or in series. The value of internal resistance r is

Question

For the two cells having same EMF E and internal resistance r, the current passing through the external resistor $6 Ω$ is same when both the cells are connected either in parallel or in series. The value of internal resistance r is ______ $Ω .$ [2026]

Smart Achievers · Accepted Answer

(1)

$In series, i_{1} = \frac{2 E}{6 + 2 r}$

$In parallel, i_{2} = \frac{E}{6 + \frac{r}{2}}$

$i_{1} = i_{2} \Rightarrow \frac{2 E}{6 + 2 r} = \frac{E}{6 + \frac{r}{2}}$

$12 + r = 6 + 2 r$

$r = 6 Ω$

Solution

Q.
For the two cells having same EMF E and internal resistance r, the current passing through the external resistor $6 Ω$ is same when both the cells are connected either in parallel or in series. The value of internal resistance r is ______ $Ω .$ [2026]

1 6

2 9

3 3

4 4

Ans.
(1)

$In series, i_{1} = \frac{2 E}{6 + 2 r}$

$In parallel, i_{2} = \frac{E}{6 + \frac{r}{2}}$

$i_{1} = i_{2} \Rightarrow \frac{2 E}{6 + 2 r} = \frac{E}{6 + \frac{r}{2}}$

$12 + r = 6 + 2 r$

$r = 6 Ω$

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Solution

Q. For the two cells having same EMF E and internal resistance r, the current passing through the external resistor 6Ω is same when both the cells are connected either in parallel or in series. The value of internal resistance r is ______ Ω. [2026]

1 6

2 9

3 3

4 4

Ans. (1) In series, i1=2E6+2r In parallel, i2=E6+r2 i1=i2⇒2E6+2r=E6+r2 12+r=6+2r r=6Ω

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Q.
For the two cells having same EMF E and internal resistance r, the current passing through the external resistor $6 Ω$ is same when both the cells are connected either in parallel or in series. The value of internal resistance r is ______ $Ω .$ [2026]

Ans.
(1)

$In series, i_{1} = \frac{2 E}{6 + 2 r}$

$In parallel, i_{2} = \frac{E}{6 + \frac{r}{2}}$

$i_{1} = i_{2} \Rightarrow \frac{2 E}{6 + 2 r} = \frac{E}{6 + \frac{r}{2}}$

$12 + r = 6 + 2 r$

$r = 6 Ω$