A. In the circuit shown in the figure, find the magnitude of current in the upper branch

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A. In the circuit shown in the figure, find the magnitude of current in the upper branch.
B. Find the magnitude of current in the middle branch.
C. Find the magnitude of current in the lower branch.
D. What is the potential difference of point a relative to point b ?

Concepts and reason
The required concepts to solve this question are Kirchhoff’s loop rule and ohm’s law.
Calculate the current in the upper, lower and middle branch by applying Kirchhoff’s loop rule.
Finally calculate the potential difference with the help of ohm’s law.

Fundamentals
The Kirchhoff’s loop rule states that the algebraic sum of the potential difference (V) in any loop must equal to zero.

The expression for the Kirchhoff’s voltage rule is,

(A)
The following figure shows a circuit diagram with resistances R,Current in the upper branch is and current in the lower branch is .

Refer the figure 1, and apply Kirchhoff’s loop rule in the loop labeled 1.

Apply Kirchhoff’s rule in the loop labeled 2.

Refer the figure 1 and determine the current in the middle branch using the following equation:

Here, I is the current in the middle branch.

(D)
Refer the figure 1 and determine the potential difference at point b.

Here, I is the current in the middle branch
Calculate the potential difference at point a using the following equation:

Calculate the potential difference between the points a and b using the following equation: