Question

The total resistance in the parallel combination of three resistances $9\Omega ,7\Omega $ and $5\Omega $ is?
A. $1.22\Omega $
B. $2.20\Omega $
C. $4.22\Omega $
D. $2.02\Omega $

Answer 1

Hint: We have studied two types of combinations of resistances that are series combination and parallel combination. In series combination the all resistances are added to find out the value of equivalent resistance while in parallel combination reciprocal value of the resistance are added to find out the reciprocal equivalent resistance.

Complete step by step answer:
In this problem it is asked to calculate the equivalent resistance of three given resistance so to find the total resistance in the parallel combination we will use this formula ; $\dfrac{1}{R} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}}$ .
Value of the given three resistance are ${R_1} = 9\Omega ,{R_2} = 7\Omega ,{R_3} = 5\Omega $
Now we will use formula $\dfrac{1}{R} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}}$ .
By putting the values of resistances in the above equation we get the value of equivalent resistance.
$
  \dfrac{1}{R} = \dfrac{1}{9} + \dfrac{1}{7} + \dfrac{1}{5} = \dfrac{{143}}{{315}} \\
  R = 2.02\Omega \\
$
Therefore, the total resistance in parallel combination is $2.02\Omega $.
Option D would be the correct answer for the following question. Hence the total resistance in the parallel combination of three resistances $9\Omega ,7\Omega $ and $5\Omega $ is $2.02\Omega $.

Note:
We know that in series combination of resistance the resistance is connected end to end in series while in parallel combination one end of all resistors are connected at the same point and other end are connected at the other point. In series combination same current flows in all resistors while voltages across the resistances differ. In parallel combination as both ends are connected at a specific point of circuit the voltage remains same across all the resistors and current differs. So here we have applied the formula of parallel combination of resistors of three resistances and calculated total resistance.