Question

Calculate the effective resistance.

A. $20\Omega $

B. $5\Omega $

C. $10\Omega $

D. $2.5\Omega $

Answer 1

Hint: An effective resistance is defined as the total resistance in the circuit that opposes the current flowing through the current. Here, in the question, four resistors are given. These resistors are connected in series forming two pairs and these pairs are parallel to each other. Therefore, here we will first use the formula of resistance in series combination and the formula of resistance in parallel combination to calculate the effective resistance in series.

FORMULA USED: The formula used for the resistance in series combination is given by ${R_S} = {R_1} + {R_2} + ......... + {R_n}$

Also, the formula used for the resistance in parallel combination is given by

$\dfrac{1}{{{R_p}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + ......... + \dfrac{1}{{{R_n}}}$

COMPLETE STEP BY STEP ANSWER:

Here, in this question, there are four resistors connected to a battery. These resistors are connected in series forming two pairs in series and these pairs are parallel to each other.

Now, we can replace the resistors that are in series to an equivalent resistor as shown below

The resistance in series are added together as shown below

${R_S} = 5 + 5$

${R_S} = 10\Omega $

That is why, in the diagram, the resistance in series after adding becomes $10\Omega $ .

Now, the resistors are parallel to each other, therefore, we will use the given formula to calculate the resistance in the circuit.

$\dfrac{1}{{{R_p}}} = \dfrac{1}{{10}} + \dfrac{1}{{10}}$

$ \Rightarrow \,\dfrac{1}{{{R_p}}} = \dfrac{{1 + 1}}{{10}}$

$ \Rightarrow \,\dfrac{1}{{{R_p}}} = \dfrac{1}{5}$

$ \Rightarrow \,{R_p} = 5\Omega $

Therefore, the effective resistance in the circuit is $5\Omega $ .

Hence, option (B) is the correct option.

NOTE: As we know that in a parallel circuit, there are two or more than two paths for the current to pass. Therefore, the sum of the currents that pass through each path will be equal to the total current flowing through the circuit. Also, the voltage applied to the series combination will be equal to the sum of individual voltages.