Question

What is the (a) highest (b) lowest resistance that can be secured by combining four coils of resistance $4\Omega ,8\Omega ,12\Omega \And 24\Omega$.

Answer 1

The highest value of resistance can be secured by combining four coils of resistance in series connection and the lowest value of resistance can be secured by combining four coils of resistance in parallel connection. The net resistance in a series connection is the sum of resistances used and the net resistance in a parallel connection, the reciprocal of equivalent resistance is the sum of reciprocals of the individual resistances.

Complete step-by-step solution: -
(a) The highest value of resistance can be secured by combining four coils of resistance in series connection.
The net resistance in a series connection is the sum of resistances used.
Hence the effective resistance in series combination can be calculated by,
$\begin{aligned} & R=4\Omega +8\Omega +12\Omega +24\Omega \\\ & \Rightarrow R=48\Omega \\\ \end{aligned}$
(b) The lowest value of resistance can be secured by combining four coils of resistance in parallel connection.
The net resistance in a parallel connection, the reciprocal of equivalent resistance is the sum of reciprocals of the individual resistances.
Hence the effective resistance in parallel combination can be calculated by,
$\begin{aligned} & \dfrac{1}{R}=\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{12}+\dfrac{1}{24} \\\ & \dfrac{1}{R}=\dfrac{6+3+2+1}{24} \\\ & \dfrac{1}{R}=\dfrac{12}{24} \\\ & \dfrac{1}{R}=\dfrac{1}{2} \\\ & \therefore R=2\Omega \\\ \end{aligned}$

Note: The net resistance in a series connection is the sum of resistances used .Whereas, the net resistance in a parallel connection, the reciprocal of equivalent resistance is the sum of reciprocals of the individual resistances. Hence while calculating the equivalent resistance, first note whether it is connected in series or parallel. Then use the suitable equation of the given circuit.