Question

For the circuit shown in the figure below, find the current through and the potential difference across each resistor. Place your results in the table for ease of reading. (Assume R1 = 27 ohm, R2 = 2 ohm, and V = 2 V.)

Answer 1

first we will calculate the total resistance and the total current flowing in the circuit

4 ohm and 12 ohm are in parallel and their parallel combination can be given as

R_p = 4 x 12 / (12 + 4) = 3 ohm

3 ohm and 5 ohm are in series and their series combination is given as ::

R_s = 3 + 5 = 8 ohm

8 ohm and R₁ are in parallel and their parallel combination is given as ::

R_p = 8 R₁ / (R₁ + 8) = 8 x 27 / (27 + 8) = 6.17 ohm

circuit now looks as

ii R -27ohm 40 50 12 12は 12! I- 2 volts R 2 ohm

Using kirchoff's law ::

6.2 i + 2 + 2i - 12 = 0

i = 1.22 A

let Voltage across R₁ = V₁

V₁ + 2 + 2 i - 12 =0

V₁ = 12 - 2 (1.22) - 2

V₁ = 7.56 volts

current in R₁ = 7.56 / 27 = 0.28 A

remaining current flowing in the lower branch = i' = 1.22 - 0.28 = 0.94

Current through 4 ohm = (12/(12 + 4)) (0.94) = 0.705

Current through 12 ohm = (4/(12 + 4)) (0.94) = 0.235

Voltage across 4 ohm = 0.705 x 4 = 2.82 volt

Voltage across 12 ohm = 0.235 x 5 = 2.82 volts

Current through 5 ohm = 0.94

Voltage across 5 ohm = 0.94 x 5 = 4.7 volts