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Kirchhoff's Junction Law

In the circui...

Question

In the circuit shown in figure, find the potentials of $A$ , $B$ , $C$ and $D$ and the current through 1 $Ω$ and 2 $Ω$ resistance.

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Solution

Since A is grounded, potential at A, $V_{a} = 0 V$
Potential at B,
$V_{b} - V_{a} = 2 V V_{b} - 0 = 2 V V_{b} = 2 V$
Potential at C,
$V_{c} - V_{a} = 5 V V_{c} - 0 = 5 V V_{c} = 5 V$
Potential at D,
$V_{d} - V_{c} = 10 V V_{d} - 5 = 5 V V_{d} = 15 V$
Since, $V_{c}$ is greater than $V_{b}$ current will flow from C to B and the magnitude will be given by
Current through $1 Ω$ resistor = $\frac{V_{c b}}{1} = 5 - 2 = 3 A$
Since, $V_{d}$ is greater than $V_{a}$ current will flow from D to A and the magnitude will be given by
Current through $2 Ω$ resistor = $\frac{V_{d a}}{2} = \frac{15 - 0}{2} = 7.5 A$

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