Question

When the switch S, in the circuit shown, is closed, then the value of current i will be-

A. 3A
B. 5A
C. 4A
D. 2A

Answer 1

Hint: In order to find the current i, we will apply the formula for current in terms of voltage and resistance. We will let the potential at node be X. Then we will put the values given in the question into the formula and find out the value of X. refer to the answer below.

Complete Step-by-Step solution:
Let the potential at node be X.
Total current i will be equal to-
$ \Rightarrow i = {i_1} + {i_2}$
Since we know that the formula to find out current in terms of voltage and resistance is $I = \dfrac{V}{R}$.
The voltage V is 0
The voltage V1 is 20V
The voltage V2 is 10V
The resistance R is 2ohm
The resistance R1 is 2ohm
The resistance R2 is 4ohm
The above values (clear from the figure) will be-
$
   \Rightarrow i = \dfrac{{X - V}}{R} \\
    \\
   \Rightarrow {i_1} = \dfrac{{{V_1} - X}}{{{R_1}}} \\
    \\
   \Rightarrow {i_2} = \dfrac{{{V_2} - X}}{{{R_2}}} \\
$
Putting these values into the formula for total current, we get-
$
   \Rightarrow \dfrac{{X - V}}{R} = \dfrac{{{V_1} - X}}{{{R_1}}} + \dfrac{{{V_2} - X}}{{{R_2}}} \\
    \\
   \Rightarrow \dfrac{{X - 0}}{2} = \dfrac{{20 - X}}{2} + \dfrac{{10 - X}}{4} \\
    \\
   \Rightarrow 2X = 2\left( {20 - X} \right) + 10 - X \\
    \\
   \Rightarrow 2X = 40 - 2X + 10 - X \\
    \\
   \Rightarrow 5X = 50 \\
    \\
   \Rightarrow X = 10V \\
$
Thus, the value of current will be-
$
   \Rightarrow i = \dfrac{{X - 0}}{2} \\
    \\
   \Rightarrow i = \dfrac{{10}}{2} \\
    \\
   \Rightarrow i = 5A \\
$
Hence, option B is the correct option.

Note: An electric current is the rate at which electric charge flows past a point or area. If there is a net flow of electrical charge through an area, an electric current is said to exist. Charged particles bear electric charge and an electrical current is a river of charged particles. The electrical current SI unit is the ampere, which is the movement of electrical charge over a surface at a rate of one coulomb per second. The ampere (symbol: A) is a unit of the SI base. Electrical current is measured using an ammeter.