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Two identical cells of EMF 1.5v each joined in series supplied to external circuit of 17ohm each joined in parallel. Terminal resistance of cells is 1.4 v calculate internal resistance

Two identical cells of EMF 1.5v each joined in series supplied to external circuit of 17ohm each joined in parallel. Terminal resistance of cells is 1.4 v calculate internal resistance

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Grade:12

1 Answers

Arun
25750 Points
5 years ago
Let r is the internal resistance of cell , E is the emf of cell. 
two cell of emf 1.5V and resistance r are in parallel also two resistors are joined in parallel with it as shown in figure. 
Terminal voltage of the = 1.4V is given . Means voltage ( V) = 1.4V are given voltage between two resistance which are joined in parallel with circuit .
Now, we have to find out equivalent resistance, 
first find equivalent resistance of two given resistors,
Req = R × R/(R + R) = R/2 = 17Ω/2 = 8.5Ω 
now, solve the circuit by applying Kirchoff's law , Let i current flow through the circuit also i₁ and i₂ Current flow through each emf.
For first loop [ assume any loop in both ]
iReq + i₁r - E = 0 
i₁ = (E - iReq)/r ----(1)
For second loop 
iReq + i₂r - E = 0 
i₂ = ( E - iReq)/r 
now, I = i₁ + i₂ = (2E - 2iReq)/r 
ir =2E - 2iReq 
i = E/(Req + r/2) 
Also V = iReq
I = V/Req = E/(Req + r/2) 
Now, put V = 1.4V , E = 1.5V , Req = 8.5Ω
1.4/8.5 = 1.5/(8.5 + r/2) 
1.4(8.5 + r/2) = 1.5 × 8.5 
r = 1.21 Ω
Hence, answer is 1.21 Ω
 
 

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