Three resistors are connected in parallel as shown in Figure (a). A potential di
ID: 1436128 • Letter: T
Question
Three resistors are connected in parallel as shown in Figure (a). A potential difference of V= 10.0 V is maintained between points a and b.
(A) Calculate the equivalent resistance of the circuit.
(B) Find the current in each resistor.
A) Calculate the equivalent resistance of the circuit.
Conceptualize Figure (a) shows that we are dealing with a simple parallel combination of three resistors.
Categorize Because the three resistors are connected in parallel, we can use the equation, 1/Req = (1/R1 + 1/R2 + 1/R3 +...), to evaluate the equivalent resistance.
Analyze Find Req:
(B) Find the current in each resistor.
The potential difference across each resistor is 10.0 V. Apply the relationshipV = IR to find the currents:
(C) Calculate the power delivered to each resistor and the total power delivered to the combination of resistors.
(C) Calculate the power delivered to each resistor and the total power delivered to the combination of resistors
Use Req to calculate the total power delivered to the same circuit with a potential difference of 12.0 V.
1 Req = 1 3.00 + 1 6.00 + 1 9.00 = 11.0 18.0Explanation / Answer
(A) Req = 18/11 = 1.63 ohm
(B) I1 = V/R1 = 10/3 = 3.33 A
I2 = V/R2 = 10/6 = 1.66 A
I3 = V/R3 = 10/9 = 1.11 A
(C)
P1 = I1^2 x R1 = (3.33 A)^2 x (3.00 ) = 33.26 W
P2 = I2^2 x R2 = (1.67 A)^2 x (6.00 ) = 16.73 W
P3 = I3^2 x R3 = (1.11 A)^2 x (9.00 ) = 11.08 W
Total power = V^2 / Req = 10 x 10 / 1.63 = 61.34 W
Total power if V = 12 V
P = V^2 / Req = (12)^2 / 1.63 = 88.34 ohm
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