Use nodal analysis in the given circuit to find Va and Vb Le

Use nodal analysis in the given circuit to find V_a and V_b. Let R₁ = 17.5 ohm, R₂ = 7 ohm, R₃ = 9.75 ohm, R₄ = 17.25 ohm, V₁ = 2 V, V₂ = 4 V, I₁ = 2 A. (Round the final answer to two decimal places.)

The voltage V_a is _____V and voltage V_b is _____V.

Solution

apply nodal analysis at node va.

(va-2)/17.5+(va-vb)/7+2=0

va[(1/7)+(1/17.5)]+vb(-1/7)=-2 ---------------------(1)

apply nodal analysis at node vb.

vb/9.75+(vb+4)/17.25+(vb-va)/7=2

va(-1/7)+vb[(1/9.75)+(1/17.25)+(1/7)]=2 ------------------(2)

from equations (1) and (2).

va=-7.972 volts.

vb=2.83 volts.