The series combination of two batteries, both of the same emf 10V, but different internal resistance of 20Ω and 5Ω, is connected to the parallel combination of two resistors 30Ω and RΩ . The voltage difference across the battery of internal resistance 20Ω is zero, the value of R. in (Ω) is......

Question

The series combination of two batteries, both of the same emf 10V, but different internal resistance of 20Ω and 5Ω, is connected to the parallel combination of two resistors 30Ω and RΩ . The voltage difference across the battery of internal resistance 20Ω is zero, the value of R. in (Ω) is...... (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

V1=ϵ 1-i⋅ r1 0=10-i× 20 i=0.5A V2=ϵ 2-ir2 =10-0.5× 5 V2=7.5V 0.5=(7 . 5/30)+(7 . 5/x) 0.5=0.25+(7 . 5/x) (7 . 5/x)=0.25 x=(7 . 5/0 . 25)=30 <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-qlo2rwmyt8wsohnk.jpg" />

V1​=ϵ1​−i⋅r1​ 0=10−i×20 i=0.5A V2​=ϵ2​−ir2​ =10−0.5×5 V2​=7.5V 0.5=307.5​+x7.5​ 0.5=0.25+x7.5​ x7.5​=0.25 x=0.257.5​=30

$V_{1} = ϵ_{1} - i \cdot r_{1}$
$0 = 10 - i \times 20$
$i = 0.5 A$
$V_{2} = ϵ_{2} - i r_{2}$
$= 10 - 0.5 \times 5$
$V_{2} = 7.5 V$
$0.5 = \frac{7.5}{30} + \frac{7.5}{x}$
$0.5 = 0.25 + \frac{7.5}{x}$
$\frac{7.5}{x} = 0.25$
$x = \frac{7.5}{0.25} = 30$