Consider the circuit shown in the figure below. (Assume R_1 = 12.0 Ohm, R_2 = 2.

Question

Consider the circuit shown in the figure below. (Assume R_1 = 12.0 Ohm, R_2 = 2.40 Ohm, and V = 6.80 V) a) Calculate the equivalent resistance of the R_1 and 5.00-ohm resistors connected in parallel. Ohm (b) Using the result of part (a), calculate the combined resistance of the R_1, 5.00 Ohm and 4.00 Ohm resistors. (c) Calculate the equivalent resistance of the combined resistance found in part (b) and the parallel 3.00- Ohm resistor. (d) Combine the equivalent resistance found in part (c) with the R_2 resistor. (e) Calculate the total current in the circuit. A (f) What is the voltage drop across the R_2 resistor? (g) Subtracting the result of part (f) from the battery voltage, find the voltage across the 3.00- Ohm resistor. V (h) Calculate the current in the 3.00- Ohm resistor. A

Explanation / Answer

a)

Rp = R1 5 /(R1 + 5) = 12 x 5/(12 + 5 ) = 3.53 ohm

b)

Rc = Rp + 4 = 3.53 + 4 = 7.53 ohm

c)

Rp' = Rc x 3 /(Rc + 3) = 7.53 x 3 /(7.53 + 3) = 2.15 ohm

d)

Req = Rp' + R2 = 2.15 + 2.40 = 4.55 ohm

e)

i = V/Req = 6.80 /4.55 = 1.5 A

f)

V = I2 R2 = I R2 = 1.5 x 2.40 = 3.6 volts

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