Determine the equivalent resistance of networks shown in the figures (a) and (b) below.

Solution

a) Equivalent resistance of network in fig. (a)

The given network is a series combination of four identical units.
Let us consider one such unit as shown in fig. One such unit is equivalent to a parallel combination of 2 Ω and 4 Ω.

Its equivalent resistance is

R_{p} = \frac{2 \times 4}{2 + 4} Ω = \frac{8}{6} Ω = \frac{4}{3} Ω

So, one unit of the given electrical network is a series combination of four resistors, each equal to

\frac{4}{3} Ω

.

Thus, the combined resistance is 4

\times

\frac{4}{3}

\frac{16}{3} Ω

\frac{16}{3} Ω or 5.33 Ω

\frac{16}{3} Ω = 5.33 Ω .

b) Equivalent resistance of network in fig (b)

Suppose a battery is connected between A and B. Same current will flow through all the resistors. So, all the resistors are connected in series.
∴ Equivalent resistance,
R_s = R + R + R + R + R = 5R

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Current Electricity

Determine the equivalent resistance of networks shown in the figures (a) and (b) below.

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