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Question: The current in the given circuit will be : ![](https://www.vedantu.com/question-sets/85ab5768-d138...

The current in the given circuit will be :

(A) 145\dfrac{1}{{45}} ampere
(B) 115\dfrac{1}{{15}} ampere
(C) 110\dfrac{1}{{10}} ampere
(D) 15\dfrac{1}{5} ampere

Explanation

Solution

Hint
To find the current in the circuit we need to find the equivalent resistance that is present in the circuit. Then by using Ohm's law with the given cell of e.m.f. of 2V and the calculated equivalent resistance we can find the current in the circuit.

Formula Used: In this solution, we will be using the following formula,
Req=R1+R2+R3+....{R_{eq}} = {R_1} + {R_2} + {R_3} + .... where Req{R_{eq}} is the equivalent resistance when the resistances are placed in series.
and 1Req=1R1+1R2+1R3+....\dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}} + .... where Req{R_{eq}} is the equivalent resistance when the resistances are placed in a parallel circuit.
And from Ohm’s law,
V=IRV = IR where VV is the potential of the cell and RR is the equivalent resistance.

Complete step by step answer
To solve the given problem we need to first find the equivalent resistances in the given circuit. Now in the circuit, we name the points as,

So in between the points A and B we can simplify the circuit as,

So on the top wire 2 resistances are in series, so the equivalent resistance is given by the formula
Req=R1+R2+R3+....{R_{eq}} = {R_1} + {R_2} + {R_3} + ....
Therefore, Req=(30+30)Ω{R_{eq}} = \left( {30 + 30} \right)\Omega
Req=60Ω\Rightarrow {R_{eq}} = 60\Omega
Now the resistance in the top and bottom wire are in parallel, so we get the equivalent resistance from the formula,
1Req=1R1+1R2+1R3+....\dfrac{1}{{{R_{eq}}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}} + ....
So substituting R1=Req=60Ω{R_1} = {R_{eq}} = 60\Omega and R2=30Ω{R_2} = 30\Omega we get
1R=1R1+1R2\dfrac{1}{R} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}}
1R=160+130\Rightarrow \dfrac{1}{R} = \dfrac{1}{{60}} + \dfrac{1}{{30}}
On doing LCM of the denominator,
1R=1+260=360\dfrac{1}{R} = \dfrac{{1 + 2}}{{60}} = \dfrac{3}{{60}}
So on taking the reciprocal we get the value of the equivalent resistance as
R=603=20ΩR = \dfrac{{60}}{3} = 20\Omega
So now in the given circuit, the resistance is R=20ΩR = 20\Omega and the potential across the cell is given in the figure, V=2VV = 2V. So from Ohm’s law, the current in the circuit is,
i=VRi = \dfrac{V}{R}
So substituting the values we get
i=220i = \dfrac{2}{{20}}
Cancelling 2 from numerator and denominator we have,
i=110Ai = \dfrac{1}{{10}}A
Therefore the correct answer is C.

Note
In the given circuit the resistances are in parallel. So the current passing gets divided into the two streams and the current in a particular stream is found by dividing the potential drop of the resistance by the resistance value. But the potential across the resistances in the two wires will be the same, that is the potential drop across the cell 2V.