Five identical cells each of internal resistance 1 Ω and emf 5 V are connected in series and in parallel with an external resistance 'R'. For what value of 'R', current in series and parallel combination will remain the same ?

Question

Five identical cells each of internal resistance 1 Ω and emf 5 V are connected in series and in parallel with an external resistance 'R'. For what value of 'R', current in series and parallel combination will remain the same ? (A) 1 Ω (B) 25 Ω (C) 5 Ω (D) 10 Ω

Tardigrade Admin · Accepted Answer

i1=(25/5+R) i2=(5/R+(1)5) i 1= i 2 ⇒ 5( R +(1/5))=5+ R 4 R =4 R =1 Ω

Q. Five identical cells each of internal resistance $1 Ω$ and emf $5 V$ are connected in series and in parallel with an external resistance ' $R$ '. For what value of ' $R$ ', current in series and parallel combination will remain the same ?

$1 Ω$

$25 Ω$

$5 Ω$

$10 Ω$

$i_{1} = \frac{25}{5 + R}$
$i_{2} = \frac{5}{R + \frac{1}{5}}$
$i_{1} = i_{2}$
$\Rightarrow 5 (R + \frac{1}{5}) = 5 + R$
$4 R = 4$
$R = 1 Ω$

Q. Five identical cells each of internal resistance 1Ω and emf 5V are connected in series and in parallel with an external resistance 'R'. For what value of 'R', current in series and parallel combination will remain the same ?

1Ω

25Ω

5Ω

10Ω