Current Electricity

JEE Main level, numerical answer, medium

276 of 380

Question 276 of 380

The equivalent resistance between the points AA and BB in the following circuit is x5Ω\frac{x}{5} \Omega. The value of xx is ____\_\_\_\_.

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Answer: 21

Using Kirchhoff's laws on the bridge circuit with resistances 6Ω,3Ω,3Ω,3Ω,6Ω6\Omega, 3\Omega, 3\Omega, 3\Omega, 6\Omega and applying a 1V test voltage:

From the loop equation:
6i1+3(2i1−i)=3(i−i1)6i_1 + 3(2i_1 - i) = 3(i - i_1)

15i1=6i⇒i1=25i15i_1 = 6i \Rightarrow i_1 = \frac{2}{5}i ...(1)

From the second loop:
3(i−i1)+6i1=13(i - i_1) + 6i_1 = 1
3i+3i1=13i + 3i_1 = 1

(3+65)i=1\left(3 + \frac{6}{5}\right)i = 1

i=521i = \frac{5}{21} A =1VReq= \frac{1V}{R_{eq}}

Req=215=4.2 ΩR_{eq} = \frac{21}{5} = 4.2 \ \Omega

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