Question

For a circuit shown in the figure, the total current in the circuit is

$\left( a \right)$ 0.1 A
$\left( b \right)$ 0.2 A
$\left( c \right)$ 18 A
$\left( d \right)$ 1 A

Answer 1

Hint: In this particular question use the concept that first find out the equivalent resistance of parallel combination then apply Ohm’s law i.e. V = IR, to calculate the current where symbols have their usual meanings, so use these concepts to reach the solution of the question.

Complete step by step answer:
We have to find out the value of current flow in the circuit as shown in the question image.
Now as we see from the figure that the voltage of the battery is 6 Volts.
Therefore, V = 6 Volts.
Now as we see from the figure that three equal resistance are connected in parallel.
Therefore, ${R_1} = {R_2} = {R_3} = 1\Omega $
So the equivalent resistance is calculated as,
$ \Rightarrow \dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}}$
Now substitute the values we have,
$ \Rightarrow \dfrac{1}{{{R_{eq}}}} = \dfrac{1}{1} + \dfrac{1}{1} + \dfrac{1}{1} = 3$
$ \Rightarrow {R_{eq}} = \dfrac{1}{3}\Omega $

Now the equivalent circuit is shown above.
Now apply a simple K.V.L in this equivalent circuit or by Ohm’s law so we have,
$ \Rightarrow V - IR = 0$
Now substitute the values we have,
$ \Rightarrow 6 - I\left( {\dfrac{1}{3}} \right) = 0$
$ \Rightarrow I\left( {\dfrac{1}{3}} \right) = 6$
$ \Rightarrow I = 6\left( 3 \right) = 18$ A.
So this is the required answer.

So, the correct answer is “Option C”.

Note: Whenever we face such types of questions the key concept we have to remember that the equivalent of parallel combination if there are n number of resistors connected in parallel is taken as $\dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}} + ...... + \dfrac{1}{{{R_n}}}$, so first find out the equivalent resistance as above then apply KVL in the equivalent circuit diagram as above and simplify we will get the required current which is flow in the circuit.