Question

The total source voltage in the circuit is 6-3i V. What is the voltage at the middle source

Answer 1

Answer:

The voltage at the middle source is $(2-4\mathbf{i})\ V$

Step-by-step explanation:

Voltage Sources in Series

When two or more voltage sources are connected in series, the total voltage is the sum of the individual voltages of each source.

The figure shown has three voltage sources of values:

$2 + 6\mathbf{i}$

$a + b\mathbf{i}$

$2 - 5\mathbf{i}$

The sum of these voltages is:

$V_t=4+a+(6+b-5)\mathbf{i}$

Operating:

$V_t=4+a+(1+b)\mathbf{i}$

We know the total voltage is $6-3\mathbf{i}$, thus:

$4+a+(1+b)\mathbf{i}=6-3\mathbf{i}$

Equating the real parts and the imaginary parts independently:

4+a=6

1+b=-3

Solving each equation:

a = 2

b = -4

The voltage at the middle source is $(2-4\mathbf{i})\ V$