Two identical cells send the same current in 3 Ω . resistance, whether connected in series or in parallel. The internal resistance of the cell should be:

Question

Two identical cells send the same current in 3 Ω . resistance, whether connected in series or in parallel. The internal resistance of the cell should be: (A)  1 Ω  (B)  3 Ω  (C)  (1/2) Ω  (D)  3.5 Ω

Tardigrade Admin · Accepted Answer

From ohms law I=(2E/2r+R) In parallel combination of two cells, the current through the external resistance r will be I=(E/(r)2+R)=(2E/2r+R) If I=I' If then 2r+R=r+2R ⇒ R=r=3 Ω

Q. Two identical cells send the same current in $3 Ω$ . resistance, whether connected in series or in parallel. The internal resistance of the cell should be:

$1 Ω$

$3 Ω$

$\frac{1}{2} Ω$

$3.5 Ω$

$\frac{3}{2} Ω$

From ohms law
$I = \frac{2 E}{2 r + R}$
In parallel combination of two cells, the current through the external resistance r will be
$I = \frac{E}{\frac{r}{2} + R} = \frac{2 E}{2 r + R}$
If $I = I^{'}$ If then $2 r + R = r + 2 R$
$\Rightarrow$ $R = r = 3 Ω$

Q. Two identical cells send the same current in 3Ω . resistance, whether connected in series or in parallel. The internal resistance of the cell should be:

1Ω

3Ω

21​Ω

3.5Ω

23​Ω

From ohms law I=2r+R2E​ In parallel combination of two cells, the current through the external resistance r will be I=2r​+RE​=2r+R2E​ If I=I′ If then 2r+R=r+2R ⇒ R=r=3Ω