Example 21.7 Three Resistors in Parallel Three resistors are connected in parallel as shown in figure (a). A potential difference of V = 12.0 V is maintained between 12 points a and b. 18.0 V (A) Calculate the 3.00 0 6.00 0 9.00 0 equivalent resistance of the circuit. 3.00 0 6.00 0 18.0 V 9.00 0 (B) Find the current in each resistor a b (a) Three resistors connected in parallel. The voltage across each resistor is 12.0 (C) Calculate the V. (b)Another circuit with three resistors and a battery. Is it equivalent to the power delivered to circuit in (a)? each resistor and the total power delivered to the combination of resistors SOLVE IT (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/Re = (1/R, + 1/R, + 1/R, +...), to evaluate the equivalent resistance. Analyze Find Re: 1 11.0 -= 3.00 0 6.00 0 9.00 0 18.0 0 Reg = 18.0 0 1.64 11.0 (B) Find the current in each resistor. The potential difference across each _AV 12.0 V= 4 A resistor is 12.0 V. Apply the relationship AV 3.00 n = IR to find the currents: I2 AV _12.0 V = 2 A R2 6.00 0 I =41 12.0 V 1.33 A R, 9.00 0 (C) Calculate the power delivered to each resistor and the total power delivered to the combination of resistors. Apply the relationship P = I'R to each 3.00 n: P = IZR, = (4.00 A) (3.00 n) = 48 resistor using the currents calculated in part (B): 6.00 0: P, = 1, 2R, = (2.00 A) (6.00 0) = 24 W 9.00 n: P, = I, 2R, = (1.33 A) (9.00 n) = 15.9 W Finalize Part (C) shows that the smallest resistor receives the most power. Summing the three quantities gives a total power of 198 W. We could have calculated this final result from part (A) by considering the equivalent resistance as follows: P = (AV) /Re= (12.0 v) /1.64 n = 88 W. MASTER IT HINTS: GETTING STARTED | I'M STUCK! Use Re, to calculate the total power delivered to the same circuit with a potential difference of 14.0 V. P = W