Question:

Consider the circuit diagram shown below, where a battery of 12 V is connected to two resistors R1 and R2 in parallel. The resistance of R1 is 2 Ω and the resistance of R2 is 3 Ω. Determine the following:

1. The equivalent resistance of the circuit.
2. The current flowing through the battery.
3. The current flowing through R1 and R2.
4. The voltage drop across R1 and R2.
5. The power dissipated by R1 and R2.

Answer:

1. To determine the equivalent resistance (Req) of the circuit, we can use the formula for resistors in parallel:

   1/Req = 1/R1 + 1/R2

   Substituting the given values:

   1/Req = 1/2 + 1/3

   1/Req = 3/6 + 2/6

   1/Req = 5/6

   Taking the reciprocal of both sides:

   Req = 6/5 Ω

   Therefore, the equivalent resistance of the circuit is 6/5 Ω.

2. The current flowing through the battery can be determined using Ohm's Law:

   I = V / Req

   Substituting the given values:

   I = 12 / (6/5)

   I = 12 * 5/6

   I = 10 A

   Therefore, the current flowing through the battery is 10 A.

3. The current flowing through R1 and R2 can be determined using the formula for resistors in parallel:

   I1 = I * (R2 / (R1 + R2))

   I1 = 10 * (3 / (2 + 3))

   I1 = 10 * (3/5)

   I1 = 6 A

   Similarly,

   I2 = I * (R1 / (R1 + R2))

   I2 = 10 * (2 / (2 + 3))

   I2 = 10 * (2/5)

   I2 = 4 A

   Therefore, the current flowing through R1 is 6 A, and the current flowing through R2 is 4 A.

4. The voltage drop across R1 and R2 can be determined using Ohm's Law:

   V1 = R1 * I1

   V1 = 2 * 6

   V1 = 12 V

   Similarly,

   V2 = R2 * I2

   V2 = 3 * 4

   V2 = 12 V

   Therefore, the voltage drop across R1 and R2 is 12 V.

5. The power dissipated by R1 and R2 can be determined using the formula:

   P = I^2 * R

   P1 = I1^2 * R1

   P1 = 6^2 * 2

   P1 = 72 W

   Similarly,

   P2 = I2^2 * R2

   P2 = 4^2 * 3

   P2 = 48 W

   Therefore, the power dissipated by R1 is 72 W, and the power dissipated by R2 is 48 W.

Note: This is a sample question and answer for educational purposes. The values and complexity can be adjusted accordingly for a real exam setting.