Question

Consider the circuit below where R1 = R4 = 5 Ohms, R2 = R3 = 10 Ohms, Vs1 = 9V, and Vs2 = 6V. Use superposition to solve for the value of V2 in volts due to Vs1 alone. Put your answer in the box below without the units. Consider the same circuit. Now, solve for V2 in volts due to the contribution of Vs2 alone. Put your answer in the box below without the units. Consider the same circuit. Now, solve for V2 in volts due to the both Vs1 and Vs2. Put your answer in the box below without the units.Figure:Resistors are connected in series and parllel

Answer 1

The value of v2 in each case is:

A) V2=3v for only Vs1

B) V2=2v for only Vs2

C) V2=5v for both Vs1 and Vs2

Step-by-step explanation:

In the attached graphic we draw the currents in the circuit. If we consider only one of the batteries, we can consider the other shorted.

Also, what the problem asks is the value V2 in each case, where:

`V_2=I_2R_2=V_(ab)`

If we use superposition, we passivate a battery and consider the circuit affected only by the other battery.

In the first case we can use an equivalent resistance between R2 and R3:

`V_(ab)'=I_1'R_(2||3)=I_1'\cdot((1)/(R_2)+(1)/(R_3))^(-1)`

And

`V_(S1)-I_1'R_1-I_1'R_4-I_1'R_(2||3)=0 \rightarrow I_1'=0.6A`

`V_(ab)'=I_1'R_(2||3)=3V=V_(2)'`

In the second case we can use an equivalent resistance between R2 and (R1+R4):

`V_(ab)''=I_3'R_(2||1-4)=I_3'\cdot((1)/(R_2)+(1)/(R_1+R_4))^(-1)`

And

`V_(S2)-I_3'R_3-I_3'R_(2||1-4)=0 \rightarrow I_3'=0.4A`

`V_(ab)''=I_3'R_(2||1-4)=2V`

If we consider both batteries:

`V_2=I_2R_2=V_(ab)=V_(ab)'+V_(ab)''=5V`