Question

In the electrical circuit shown in the figure the current through the 4Ω resistor is:

A. 1 A
B. 0.5 A
C. 0.25 A
D. 0.1 A

Answer 1

Hint: We will find the equivalent resistances of different branches using the formulas for series and parallel connections and then use them to find the current in the circuit and then calculate the amount of current that passes through the 4 ohm resistor.

Formula used:
ohm’s law
V = IR
Total resistance in series connection
\[R={{R}_{1}}+{{R}_{2}}\]
Total resistance in parallel connection
\[\dfrac{1}{R}=\dfrac{1}{{{R}_{1}}}+\dfrac{1}{{{R}_{2}}}\]

Complete step by step answer:
First, we will find the net resistance of the 3 resistors in series on the right side

R = 2+4+2 = 8
Now we will find the net resistance due to the two 8-ohm resistors in parallel connection. The resistors in the red circle add to 8 ohm.

$\dfrac{1}{R}=\dfrac{1}{8}+\dfrac{1}{8}=\dfrac{2}{8}\Rightarrow R=4$
Finally, there are 3 resistors in series, the two 3-ohm resistors and one 4-ohm resistor (The equivalent of resistors in red and green circles above)
Final resistance = 3+4+3 = 10 ohm
So, using ohm’s Law we get the total current through the circuit as
$V=IR\Rightarrow 9=10I\Rightarrow I=0.9$A
This whole current passes through the 3-ohm resistor and then it gets divided between the 8 ohm resistor and the combination of the three resistors equivalent to 8 ohm. As the resistance on both the branches is the same the current will be divided equally between them. So, 0.45 ampere of current will pass through both the branches. As there are no further divisions, the same amount of current will flow through the complete branch and this will be the current that is passed through the 4 ohm resistor. None of the options match the correct answer. So, we will choose the closest answer.
Hence, the correct option is B, i.e. 0.5 A.

Note:
We can also use the loop rule in both the loops along with junction rule to solve. There we will have to solve a system of linear equations and that method will be longer and take more time. Therefore, this method of finding equivalent resistances and using ohm’s law is easier to solve.