Question 2.SA.1: Determine the following for the DC circuit shown below if R1......
Determine the following for the DC circuit shown below if R_1 = 5 Ω, R_2 = R_3 = 10 Ω, and R_4 = R_5 = 20 Ω:
a. Current flowing through resistor R_1
b. Voltage across resistor R_5
a. R_{eq} was derived in Example 1.2 as follows:
Combination of R_2 and R_4 = R_{2,4} = R_2 + R_4 = 10 Ω + 20 Ω = 30 Ω
Combination of R_3 and R_5 = R_{3,5} = R_3 + R_5 = 10 Ω + 20 Ω = 30 Ω
Combination of R_{2,4} and R_{3,5} = R_{2- 5}=\frac{(30 Ω).(30 Ω)}{(30 Ω+30 Ω )}=\frac{900}{60}=15 Ω
R_{eq}=R_1+R_{2- 5}= 5 Ω +15 Ω = 20 ΩCurrent through R_1 would be the same as the current through the 12 V supply:
I=\frac{V}{R_{eq}}=\frac{12 V}{20 Ω}= 0.6 Ab. One method for determining V_{R5}, voltage across R_5, is to first calculate V_{R2–5}, the voltage across the combined resistance of resistances R_2, R_3,R_4, and R_5. Then, by applying voltage division, calculate V_{R5}:
According to Ohm’s law:
Then, by applying the voltage division rule:
V_{R5}=(9 V).\left\lgroup \frac{R_5}{R_5 +R_3}\right\rgroup=(9 V).\left\lgroup \frac{20 Ω}{20 Ω +10 Ω}\right\rgroup
= (9 V) .(0.67) = 6 V