Question

Below is a circuit schematic of sources and resistors (Figure 3). VS = 10V , R1 = 100Ω, R2 = 50Ω, R3 = 25Ω, IS = 2A. Calculate the voltage V3 and the current i1 in amps that goes through R3 from left to right.

Answer 1

`V_3\approx 4.28\,\,V`

`I_1=0.0572\,\,amps`

`I_3\approx 0.171\,\,amps`

Step-by-step explanation:

Notice that this is a circuit with resistors R1 and R2 in parallel, connected to resistor R3 in series. It is what is called a parallel-series combination.

So we first find the equivalent resistance for the two resistors in parallel:

`(1)/(Re)= (1)/(R1)+(1)/(R2)\\(1)/(Re)= (1)/(100)+(1)/(50)\\(1)/(Re)= (3)/(100)\\Re=(100)/(3) \,\,\Omega`

By knowing this, we can estimate the total current through the circuit,:

`Vs=I\,*\,((100)/(3) +25)\\10=I\,*\,(175)/(3) \\I=(30)/(175) \,amps`

So approximately 0.17 amps

and therefore, we can estimate the voltage drop (V3) in R3 uisng Ohm's law:

`V_3=(30)/(175) *\,25=(30)/(7) \approx 4.28\,\,V`

So now we know that the potential drop across the parellel resistors must be:

10 V - 4.28 V = 5.72 V

and with this info, we can calculate the current through R1 using Ohm's Law:

`I_1=(V_1)/(R_1) =(5.72)/(100) =0.0572\,\,amps`