A dc source of emf E1 = 100 V and internal resistance r = 0.5 Ω, a storage battery of emf E2 = 90 V and an external resistance R are connected as shown in figure. For what value of R no current will pass through the battery ?

Question

A dc source of emf E1 = 100 V and internal resistance r = 0.5 Ω, a storage battery of emf E2 = 90 V and an external resistance R are connected as shown in figure. For what value of R no current will pass through the battery ? (A) 5.5 Ω (B) 3.5 Ω (C) 4.5 Ω (D) 2.5 Ω

Tardigrade Admin · Accepted Answer

(100/R+r)= (90/R) ⇒ (R+r/R)=(10/9) ⇒ 1+(0.5/R)=(10/9) (0.5/R)=(1/9) ∴ R=4.5 Ω

Q. A dc source of emf $E_{1} = 100 V$ and internal resistance $r = 0.5 Ω$ , a storage battery of emf $E_{2} = 90 V$ and an external resistance $R$ are connected as shown in figure. For what value of $R$ no current will pass through the battery ?

$5.5 Ω$

$3.5 Ω$

$4.5 Ω$

$2.5 Ω$

$\frac{100}{R + r} = \frac{90}{R}$
$\Rightarrow \frac{R + r}{R} = \frac{10}{9}$
$\Rightarrow 1 + \frac{0.5}{R} = \frac{10}{9}$
$\frac{0.5}{R} = \frac{1}{9}$
$∴ R = 4.5 Ω$

Q. A dc source of emf E1​=100V and internal resistance r=0.5Ω, a storage battery of emf E2​=90V and an external resistance R are connected as shown in figure. For what value of R no current will pass through the battery ?

5.5Ω

3.5Ω

4.5Ω

2.5Ω