Find the potential difference across each resister in figure.

Find the potential difference across each resister in figure if R₁=5Ω, R₂=4Ω, R₃=3Ω, R₄=2Ω.

Solution

Applying Kirchhoff’s Current Law:

I₁-I₂-I₃=0 ……..(1)

Applying Kirchhoff’s Voltage Law in loop (1)

-3-4I₂-5I₁+12=0

Or, 4I₂+5I₁-9=0 ………(2)

Applying Kirchhoff’s Voltage Law in loop (2)

-18-2I₃+4I₂+3=0

Or, 5I₃-4I₂+15=0 ……….(3)

Solving these equations, we get:

I₁=$\frac{{21}}{{65}}$

I₂=$\frac{{24}}{{13}}$

I₃= -$\frac{{99}}{{65}}$ [Negative sign shows the direction of current is opposite of our assumption.]

From Ohm’s Law

${V_{{R_1}}}$=5 R₁=5×$\frac{{21}}{{65}}$ =1.61V

${V_{{R_2}}}$=4 R₂=4×$\frac{{24}}{{13}}$ =7.38V

${V_{{R_3}}}$=3 R₃=3×$\frac{{99}}{{65}}$ =4.56V

${V_{{R_4}}}$=2 R₄=2×$\frac{{99}}{{65}}$ =3.046