Four resistors are connected as shown in figure (a). (A) Find the equivalent resistance between points a and 6.0 0 /8.0 0 Th (B) What is the current in each resistor if a potential 4.0 02 difference of 36 V is maintained between a and c? SOLVE IT 3.0 0 (A) Find the equivalent resistance between points a and C. Conceptualize Imagine charges flowing into this 120 0% 1200 combination from the left. All charges must pass - MW through the first two resistors, but the charges split into two different paths when encountering the combination of the 6.0 0 and the 3.0 0 resistors. Categorize Because of the simple nature of the 14.0 0 combination of resistors in the figure, we categorize this C example as one for which we can use the rules for series and parallel combinations of resistors. The original network of resistors is reduced to a single equivalent resistance. Analyze The combination of resistors can be reduced in steps as shown in the figure. Find the equivalent resistance between a R = 3.0 0 + 4.0 0 = 7.0 0 and b of the R = 3.0 0 and 4.0 0 resistors, which are in series: Find the equivalent resistance between b 1 1 1 3 and c of the 6.0 0 and 3.0 0 resistors, Re -6.on 3.0 0 6.0 0 which are in parallel: 3 R=6.0 1= 2.0 0 The circuit of equivalent resistances now Re = 7.0 0 + 2.0 0 = 9.0 looks like figure (b). Find the equivalent resistance from a to ci This resistance is that of the single equivalent resistor in figure (c). (B) What is the current in each resistor if a potential difference of 36 V is maintained between a and c ? The currents in the 3.0 0 and 4.0 0 resistors are the same because they are in series. In addition, they carry the same current that would exist in the 9.0 0 equivalent resistor subject to the 36 V potential difference. Use the equation: (R = 4//!) and the AV 36 V result from part (A) to find the current in I =- ac Reg 9.0 0 the 3.0 0 and 4.0 0 resistors: I = 4.0 A Set the voltages across the resistors in AV, = AV2 - (6.0 0) 1, = (3.0 0)12 - 12 = 21, parallel in figure (a) equal to find a relationship between the currents: Use I, + 1, = 4.00 A to find I, : I, + 1, = 4.00 A - I, + 21, = 4.00 A - I, = 1.33 VA Find I2: I2 = 21 = 2(1.33 A) = 2.66 A Finalize As a final check of our results, note that Ab = (6.0 0), = (3.0 0), = 8.0 V and AV = (7.0 0)1 = 28.0 V; therefore, AV= AV ,+ Al , as it must. MASTER IT HINTS: GETTING STARTED | I'M STUCK! Find the equivalent resistance of the following combination of resistors where R, = 5.2 0, R, = 7.1 0, R, = 3.2 0, and R. = 6.50. Reg n R. R