Chapter 23, Problem 40A

To determine

To Explain:The reason for the difference in the equivalent resistance between three resistors connected in series and in parallel.

Explanation of Solution

Introduction:

In a parallel connection circuit, the voltage drop across each branch remains same.In a series circuit, the current in the circuit is same and the voltage across each resistor drops. The current in the circuit is equal to the voltage provided by the power source divided by the equivalent resistance of the circuit.

Equivalent resistance for parallel combination can be obtained by:

  $\begin{array}{c}{R}_{eq}={\left[\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\mathrm{....}\right]}^{-1}\\ ={\left[\frac{1}{60}+\frac{1}{60}+\frac{1}{60}\right]}^{-1}\\ =20\Omega \end{array}$

Equivalent resistance for series combination can be obtained by:

  $\begin{array}{c}{R}_{eq}=R_1+R_2+R_3+\mathrm{...}\\ =60+60+60\\ =180\Omega \end{array}$

Conclusion:

The equivalent resistance for a parallel connection circuit is less than that of series circuit.