Question

Calculate the equivalent resistance between A and B in the given figure. Please Answer with explanation.

Answer 1

Let R1 = 3 ohm

R2 = 10 ohm

R3 = 6 ohm

R4 = 20 ohm

R5 = 100 ohm

This structure is a Wheatstone Bridge.

But we don't know if its balanced or not.

For bridge to be balanced the resistances ratios should be equal as below

$\frac{R1}{R2}$ = $\frac{R3}{R4}$

Since $\frac{3}{10}$ = $\frac{6}{20}$

Hence it is a balanced wheatstone bridge

Under balanced condition no current flows throught the middle branch we can omitt that resistance and hence our circuit reduces with R1 and R3 in series in parallel to series combination of R2 and R4.

$\frac{1}{R}$ = $\frac{1}{9}$ + $\frac{1}{30}$

$\frac{1}{R}$ = $\frac{10 + 3}{90}$

R = $\frac{90}{13}$

R = 6.92 ohms