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Question

Two identical cell of emf 1.5 V each joined in parallel provide supply to an external circuit consisting of resistances of 17 Ω each joined in parallel. A very high resistance voltmeter reads the terminal voltage of the cells to be 1.4 V. What is the internal resistance of each cell ?

A
1.5Ω
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B
1Ω
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C
1.2Ω
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D
2Ω
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Solution

The correct option is B 1.2Ω
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+irE=0
i=(EiReq)r ----(1)
For second loop
iReq+irE=0
i=(EiReq)/r
now, I=i+i=(2E2iReq)/r
ir=2E2iReq
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
1.48.5=1.5/(8.5+r/2)
1.4(8.5+r/2)=1.5×8.5
r=1.21Ω

Hence, answer is 1.21Ω

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