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

Question

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

Tardigrade Admin · Accepted Answer

E1=E-ir E2=E-ir = 10 - i20 = 0 = 10 - 0.5 Ã 5 i = 0.5 A =7.5 V Enet=E1+E2=7.5 V i=i1+i2 0.5=(7.5/x)+(7.5/30) x=30 Ω

E1​=E−irE2​=E−ir =10−i20=0=10−0.5×5 i=0.5A=7.5V Enet​=E1​+E2​=7.5V<br/>i=i1​+i2​ 0.5=x7.5​+307.5​ x=30Ω

$E_{1} = E - i r E_{2} = E - i r$
$= 10 - i 20 = 0 = 10 - 0.5 \times 5$
$i = 0.5 A = 7.5 V$
$E_{n e t} = E_{1} + E_{2} = 7.5 V < b r / > i = i_{1} + i_{2}$
$0.5 = \frac{7.5}{x} + \frac{7.5}{30}$
$x = 30 Ω$