Two identical cells of emf 1.5v each joined in parallel, provide supply to an external circuit consisting of two resistors of 17 ω.each joined in parallel. a very high resistance voltmeter reads the terminal voltage of the cells to be 1.4v. what is the internal resistance of each cell?
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Let internal resistance of cell is r .
Then, 1/rₐ = 1/r + 1/r = 2/r , here rₐ is the equivalent resistance of cells .
Now, equivalent resistance of r₁ and r₂
1/R = 1/r₁ + 1/r₂ = 1/17 + 1/17 = 2/17
R = 17/2 = 8.5 Ω
Given, emf of cell , ξ = 1.5V,
Reading of terminal voltage of cell , V = 1.4V
Now, solve the circuit ,
V = ξ - irₐ
Here, i = V/R ∴ V = ξ - (V/R)rₐ
now, put all values ,
1.4 = 1.5 - (1.4)/8.5 × r/2 [ ∵ rₐ = r/2 ]
- 0.1 =- 0.7/8.5 × r
r = 8.5/7 = 1.2Ω
Hence, internal resistance is 1.2Ω
Then, 1/rₐ = 1/r + 1/r = 2/r , here rₐ is the equivalent resistance of cells .
Now, equivalent resistance of r₁ and r₂
1/R = 1/r₁ + 1/r₂ = 1/17 + 1/17 = 2/17
R = 17/2 = 8.5 Ω
Given, emf of cell , ξ = 1.5V,
Reading of terminal voltage of cell , V = 1.4V
Now, solve the circuit ,
V = ξ - irₐ
Here, i = V/R ∴ V = ξ - (V/R)rₐ
now, put all values ,
1.4 = 1.5 - (1.4)/8.5 × r/2 [ ∵ rₐ = r/2 ]
- 0.1 =- 0.7/8.5 × r
r = 8.5/7 = 1.2Ω
Hence, internal resistance is 1.2Ω
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