A circuit is constructed with five resistors and a battery as shown. The values

Question

A circuit is constructed with five resistors and a battery as shown. The values for the resistors are: R_1 = R_5 = 56 ohm, R_2 = 130 ohm, R_3 = 81 ohm, and R_4 = 85 ohm. The battery voltage is V = 12 V. What is R_ab, the equivalent resistance between points a and b? What is R_ac, the equivalent resistance between points a and c? What is l_5, the current that flows through resistor R_5? What is I_2, the current that flows through resistor R_2? What is I_1, the current that flows through the resistor R_1? What is V_4, the voltage across resistor R_4?

Explanation / Answer

a)

R2 and R3 are in series and their combination is given as

R23 = R2 + R3 = 130 + 81 = 211 ohm

Rab = R23 = 211 ohm

b)

R23 and R4 are in parallel and their combination is given as

R234 = R23 R4 /(R23 + R4) = 211 x 85 /(211 + 85) = 60.6 ohm

R1 and R234 are in series and their combination is given as

R1234 = R1 + R234 = 56 + 60.6 = 111.6 ohm

Rac = R1234 = 111.6 ohm

3)

R5 and R1234 are in series and their combination is given as

R12345 = R1234 + R5 = 111.6 + 56 = 167.6 ohm

V = battery voltage = 12 volts

since R5 is in series with the battery ,

I5 = V/R12345 = 12 /167.6 = 0.072 A

4)

i1 = i5 = 0.072 A

V1 = Voltage in R1 = i1 R1 = 0.072 x 56 = 4.03 volts

V5 = 4.03 volts

V4 = V - V1 - V5 = 12 - 4.03 - 4.03 = 3.94 volts

i4 = V4/R4 = 3.94 /85 = 0.046 A

i2 = i1 - i4 = 0.072 - 0.046 = 0.026 A

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