Question

Four resistances of 16 ohms each are connected in parallel. Four such combinations are connected in series. What is the total resistance ?

Answer 1

for parallel combinations 1/R= 1/16+1/16+1/16+1/16=1/4 i.e. 1/R=1/4 or R=4 ohm
for series R'= 16+16+16+16=64
so total resistance is
R+R'= 4+64=68 ohms

Answer 2

The total resistance is 16 ohm.

Given data:

4 resistances is in parallel connection, each of resistor is of 16 ohm

Other 4 combinations of same type are connected in series.

Solution:

The parallel combination has an effective total resistance as given below:

$\frac{1}{R} = \frac{1}{16} + \frac{1}{16} + \frac{1}{16} + \frac{1}{16}$

$\frac{1}{R} = \frac{4}{16}$

$\frac{1}{R} = \frac{1}{4}$

Therefore, the total resistance of parallel connected, R = 4 ohm

Now, the total effective resistance of resistance in series connection, we have

R’ = 4 + 4 + 4 + 4

$\Rightarrow$ R’ = 16