Question

What is the combined resistance of a 6 ohm resistor which is connected in series with a parallel arrangement of two resistors, each resistance of 2 ohm?

Answer 1

In the question it is given that a 6 ohm resistor is connected in series with a combination of two parallel 2 ohm resistors which are connected in parallel. In order to solve this question, first we will calculate the net resistance of the two parallel resistors. Then this net resistance will be in series with the 6 ohm resistor. On applying the formula for the series resistance, we will get the combined resistance of this circuit.

Complete step by step answer:
The diagram for this circuit is as follows:

Let us consider the three resistances as,
${R_1} = 6\Omega$
${R_2} = 2\Omega$
${R_3} = 2\Omega$
Now, let us first find the net resistance of the two resistances which are in parallel,
$\frac{1}{{{R_P}}} = \frac{1}{{{R_2}}} + \frac{1}{{{R_3}}}$
Here, ${R_2} = 2\Omega$ and ${R_3} = 2\Omega$
On putting the above values in the equation,
$\frac{1}{{{R_P}}} = \frac{1}{2} + \frac{1}{2}$
$\frac{1}{{{R_P}}} = \frac{{1 + 1}}{2}$
On further solving, we get,
$\frac{1}{{{R_P}}} = \frac{2}{2}$
$\frac{1}{{{R_P}}} = 1$
On taking the reciprocal,
${R_P} = 1\Omega$
Now, ${R_P}$ and ${R_1}$ are in a series combination, so,
${R_{eq}} = {R_P} + {R_1}$
On putting the required values, we get,
${R_{eq}} = 1 + 6$
${R_{eq}} = 7\Omega$
So, the combined resistance of this circuit is ${R_{eq}} = 7\Omega$

Note: In a series circuit of resistances, the current is said to be same throughout all the resistors irrespective of the component as the series circuits do not have any break or any kind of nodal division in the circuit which causes the current to flow in more than one direction. Hence, the current is the same in all the resistances. Whereas in a parallel circuit, the current is divided among the resistances and the current is not the same in all the resistances.