201902190342 Electric circuit diagrams (Elementary) Q9

The blogger claims no originality of his question below.

Find the equivalent resistance between nodes a and b.

Circuit0007


Solution.

The equivalent resistance of two R‘s in series is 2R:

Circuit0007Sol001

The equivalent resistance of R and 2R in parallel is R_{\mathrm{eq}}=\displaystyle{\frac{(R)(2R)}{R+2R}}=\displaystyle{\frac{2}{3}R}:

Circuit0007Sol002

For R and \displaystyle{\frac{2R}{3}} in series, R_{\mathrm{eq}}=\displaystyle{\frac{5}{3}R}:

Circuit0007Sol003

Finally, the equivalent resistance between nodes a and b is R_{\mathrm{eq}}=\displaystyle{\frac{R\bigg( \displaystyle{\frac{5}{3}R}\bigg)}{R+\displaystyle{\frac{5}{3}R}}}=\displaystyle{\frac{5}{8}R}.

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