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## Q. 6.9

Determine the total resistance of the parallel elements in Fig. 6.13.

## Verified Solution

The network is redrawn in Fig. 6.14.

Eq. (6.4):     $R^{\prime }_T=\frac{R}{N}=\frac{6\Omega }{3}=2\Omega$

Eq. (6.5):     $R^{\prime \prime }_T=\frac{R_2R_4}{R_2+R_4}=\frac{(9\Omega )+(72\Omega ) }{9\Omega +72\Omega }=\frac{648 }{81}\Omega=8\Omega$

Eq. (6.5):     $R_T=\frac{R^{\prime }_TR^{\prime \prime }_T}{R^{\prime }_T+R^{\prime \prime }_T}=\frac{(2\Omega )+(8\Omega ) }{2\Omega +8\Omega }=\frac{16 }{10}\Omega=1.6\Omega$