Question

assuming the information in the following tables is pulled from the simple parallel circuit below, find all missing resistances, voltages, and currents.
#1 v (v) i (a) r (ω)
1 4
2 13
3 8
t 100

Explanation:

Step1: Recall parallel - circuit rules

In a parallel circuit, the voltage across each resistor is the same as the total voltage. So \(V_1 = V_2=V_3 = V_T = 100V\).

Step2: Calculate resistance for Row 1

Using Ohm's law \(R=\frac{V}{I}\), for Row 1 with \(V = 100V\) and \(I = 4A\), we have \(R_1=\frac{100}{4}=25\Omega\).

Step3: Calculate resistance for Row 2

Using Ohm's law \(R=\frac{V}{I}\), for Row 2 with \(V = 100V\) and \(I = 13A\), we have \(R_2=\frac{100}{13}\approx7.69\Omega\).

Step4: Calculate resistance for Row 3

Using Ohm's law \(R=\frac{V}{I}\), for Row 3 with \(V = 100V\) and \(I = 8A\), we have \(R_3=\frac{100}{8}=12.5\Omega\).

Step5: Calculate total current

The total current \(I_T=I_1 + I_2+I_3=4 + 13+8=25A\).

Answer:

#1	V (V)	I (A)	R (\(\Omega\))
2	100	13	\(\frac{100}{13}\approx7.69\)
3	100	8	12.5
T	100	25	-