Question

Its given that r1>r2 . If Va=Vb then find external Resistance R
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Answer 1

Given:

r1 > r2 , and V_(A) = V_(B) .

To find:

External resistance R ?

Calculation:

First of all, find the net current through circuit:

$\rm \therefore \: i = \dfrac{2E}{r1 + r2 + R} \: \: \: \: . \: . \: . \: . \: .(1)$

Now, apply Kirchhoff's Voltage Law from point A to point B :

$\rm \therefore \: V_{A} - E + i(r1) = V_{B}$

$\rm \implies \: \cancel{V_{A}} - E + i(r1) = \cancel{V_{B}}$

$\rm \implies \: E = i(r1)$

$\rm \implies \: E = \bigg \{ \dfrac{2E}{r1 + r2 + R} \bigg \} (r1)$

$\rm \implies \: r1 + r2 + R = 2(r1)$

$\boxed{ \rm \implies \: R = r1 - r2}$

This is the easiest way to solve this problem! Try to remember this expression, as it's often asked in NEET !