If a cell of internal resistance 1-5 - and emf of 1-5 V balances 500 cm on a potentiometer wire- now by what length would the balance point shift if a cell of internal resistance 2 - and emf of 2 V is connected in parallel along the same polarity with the prior cell-A- 71-4 cm towards leftB- 71-4 cm towards rightC- 125 cm towards rightD- Does not shift

The correct option is B 71.4 cm towards rightCase 1: Case 2: using nbsp;kirchhoff's current law: i=E/r_equi=E_1/r_1+E_2/r_2 =1+1=2 total resistance= 2 × 1 ...

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Byju's Answer

Standard XII

Physics

Series and Parallel Combination of Resistors

If a cell of ...

Question

If a cell of internal resistance $1.5 Ω$ and emf of $1.5 V$ balances $500 c m$ on a potentiometer wire, now by what length would the balance point shift if a cell of internal resistance $2 Ω$ and emf of $2 V$ is connected in parallel (along the same polarity) with the prior cell?

71.4 c m

towards left

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71.4 c m

towards right

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125 c m

towards right

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Does not shift

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Solution

The correct option is B $71.4 c m$ towards right
Case-1:
Case-2:

using kirchhoff's current law:
$i = \frac{E}{r_{e q u i}} = \frac{E_{1}}{r_{1}} + \frac{E_{2}}{r_{2}} = 1 + 1 = 2$
total resistance= $\frac{2 \times 1.5}{2 + 1.5} = \frac{6}{7}$

So, the EMF of the circuit,
$\frac{7 E}{6} = 2 E = \frac{12}{7}$
Here, extra emf is adding for balancing, hence meter point will move towards right.

for the case-1
$1.5 \to 500 c m$
$\frac{12}{7} \to \frac{12 / 7 \times 500}{1.5} = 571.4 c m$

Now, the shift of the meter $Δ x = 571.4 - 500 = 71.4 c m$

so, option B is correct.

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If a cell of internal resistance 1.5 Ω and emf of 1.5 V balances 500 cm on a potentiometer wire, now by what length would the balance point shift if a cell of internal resistance 2 Ω and emf of 2 V is connected in parallel (along the same polarity) with the prior cell?

If a cell of internal resistance $1.5 Ω$ and emf of $1.5 V$ balances $500 c m$ on a potentiometer wire, now by what length would the balance point shift if a cell of internal resistance $2 Ω$ and emf of $2 V$ is connected in parallel (along the same polarity) with the prior cell?