Question

Find the equivalent resistance of the networks shown in Fig. 4.51 between the points A and B.

Answer 1

Correct Answer - `(4)/(3) r (b) (r )/(4) ( c) r`

Answer 2

(a) \(\frac 1R = \frac1r + \frac1 r + \frac1r\)

\(\frac 1R = \frac3r\)

\(R = \frac r3\)

\(R = \frac r3 + r\)

\(R = \frac{4r}3\)

(b) \(\frac 1R = \frac1r + \frac1 r \)

\(\frac 1R = \frac2r\)

\(R = \frac r2\)

\(\frac 1R = \frac1r + \frac1 r \)

\(\frac 1R = \frac2r\)

\(R = \frac r2\)

then

\(\frac 1R = \frac1R + \frac1 R\)

\(\frac 1R = \frac2r + \frac2r \)

\(\frac 1R = \frac4r\)

\(R = \frac r4\)

(c) \(R = r + r + r + r\)

\(R_1 = 4r\)

\(\frac 1R = \frac1r + \frac1 r \)

\(R_2 = \frac r2\)

then

\(R = R_1 + R_2\)

\(R = 4r + \frac r2\)

\(R = \frac{9r}2\)