In the circuit shown below, the emf of the battery is E = 7.2 volts. Resistor R_
ID: 1535138 • Letter: I
Question
In the circuit shown below, the emf of the battery is E = 7.2 volts. Resistor R_1 has a resistance of 33 ohms, resistor R_2 has a resistance of 45 ohms, and resistor R_3 has a resistance of 51 ohms. A steady current flows through the circuit. What is the equivalent resistance of R_1 and R_2? what is the equivalent resistance of all the resistors: R_1, R_2, and R_3? What is the conventional current through R_3? What is the power dissipated in each resistor? If another battery with emf of E = 10.0 volts is added across R_2 (Positive up), then what is the current in R_3?Explanation / Answer
(a)In the circuit consider
R1 , R2 are in parallel
R12 = R1*R2/(R1+R2) = (33*45)/(33+45) = 19 ohms
(b)
Consider
R12 , R3 are in series
Req = R12 + R3 = 19 + 51 = 70 ohms
(c)
current through R3 , I3 = E/Req = 7.2/70 = 0.10 A
current through R1 , I1 = V1/R1 = I3*R12/R1 = 0.1*19/33 = 0.06 A
current through R2 , I2 = I3 - I1 = 0.04 A
(d)
P1 = I1^2*R1 = 0.06^2*33 = 0.12 W
P2 = I2^2*R2 = 0.04^2*45 = 0.07 W
P3 = I3^2*R3 = 0.1^2*51 = 0.51 W