The circuit in the figure connects for two minutes. a. Determine the current in

Question

The circuit in the figure connects for two minutes.
a. Determine the current in each branch of the circuit.
b. Determine the energy that each battery loses. c. Determine the energy each resistor receives. The circuit in the figure connects for two minutes.
a. Determine the current in each branch of the circuit.
b. Determine the energy that each battery loses. c. Determine the energy each resistor receives.
a. Determine the current in each branch of the circuit.
b. Determine the energy that each battery loses. c. Determine the energy each resistor receives. 5.00 3.00 1.00 1.00 8.00

Explanation / Answer

here,

let the current through 4 V and 12 V be i1 and i2

using KVl in the right side loop

( 3 + 1) * i2 - ( 5 + 1) * i2 = 12 - 4 ....(1)

and

using KVL in the left side loop

( 5 + 1) * i1 + 8 * (i1 + i2) = 4 .....(2)

from (1) and (2)

i1 = 0.76 A

i2 = - 0.83 A

the current through 8 ohm , i3 = i1 + i2 = - 0.07 A

b)

time taken , t = 2 min = 120 s

the energy through 4 V battery , E1 = 4 V * i1 * t = 364.8 J

the energy through 12 V battery , E2 = 12 V * i2 * t = 1195.2 J

c)

the energy through 8 ohm , E3 = i3^2 * 8 * t = 4.7 J

the energy through 5 ohm , E4 = i1^2 * 5 * t = 346.6 J

the energy through 1 ohm , E5 = i1^2 * 1 * t = 69.3 J

the energy through 1 ohm close to 12 V battery , E6 = i2^2 * 1 * t = 82.7 J

the energy through 3 ohm , E7 = i2^2 * 3 * t = 248 J

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