In the circuit given below, all resistor values are in ohms. Find the voltage across 10 ohms resistor.

Concept:

Nodal Analysis:

• Nodal Voltage Analysis uses the “Nodal” equations of Kirchhoff’s first law to find the voltage potentials around the circuit. So by adding together all these nodal voltages the net result will be equal to zero.

Let a network and find voltage V using nodal analysis

Applying nodal analysis at node V

\(\frac{{V - {V_1}}}{{{R_1}}} + \frac{{V - {V_2}}}{{{R_2}}} + \frac{{V - {V_3}}}{{{R_3}}} = 0\)

By solving it we can find voltage V

Calculation:

Apply Nodal at node A, we get:

\(\frac{{{V_A}}}{{40}} - 0.25 + \frac{{{V_A} - 5}}{{10}} = 0\)

\(\frac{{{V_A}}}{{40}} + \frac{{{V_A}}}{{10}} = 0.75\)

5V_A = 0.75 × 40

V_A = 6V

The voltage across 10 Ω is,

V_{10 Ω} = V_A – V_B = 6 – 5 = 1V