In this example we will use the concept of equivalent resistance to determine th

Question

In this example we will use the concept of equivalent resistance to determine the current in a circuit. Three identical resisters within emf of 18.0 V and zero internal resistance (a) Find the equivalent resistance of the resistor network (b) Find the current in each resistor. R_eq - R_1 + R_23 = 6.0 Ohm + 3.0 Ohm = 9.0 Ohm Thus, the equivalent resistance of the entire network is 9.0 Ohm To find the current and voltages, we work backward, as shown is (Figure 5) starting with the single equivalent resistor, in the voltage across R_eq is because the battery has 65 internal resistance also IR_eq so I = epsilon/R_eq = 18.0 V/9.0 Ohm = 2.0 A. This is the current through the battery and also the total current through the network R_1, R_23, and the battery are in series, so the same 2.0 A current passes through each. The voltage V_1 across R_1 is V_1 - 1R_1 = (2.0A) (6.0 Ohm) = 12.0 V The voltage V_23 across R_23 is V_23 - 1R_23 = (2.0 A) (3.0 Ohm) = 6.2 V The voltage across the parallel combination of R_2 and R_3 is the potential difference between points c and d, which is V_23 = 6.0 V, since the voltage across R_2 + is 6.0 V we can calculate the current I_3 through R_2 I_2 = 6.0 V/6.0 Ohm 10 A A similar calculation give the current I_2 through R_3 I_3 = 6.0 V/6.0 Ohm = 1.0 A. In summary, I_2 2.0 A and I_2 = 1.0A. The two identical resistors R_2 and R_3 form a parallel combination the 2.0 A current arriving at point c in the circuit divides equally;10 A currents recombine into a 2.0 A current What is the current through R-1 in the network in this example if the resistors equal but instead R_1 = 3.0 Ohm R_3 = 430 Ohm, and R_3 = 2.0 Ohm?

Explanation / Answer

(a)

R2 and R3 are parallel.

so, Rp = 6*6 / (6+6) = 3 ohm

This is in series with R1.

so, Req = 3 + 6 = 9 ohm

(b)

Total current in circuit,

l = V / R = 18 / 9

l = 2 A

current through R1 = 2 A

R2 and R3 are parallel and have equal resistance. so current will divide equaly.

lR2 = lR3 = 1 A

answer

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