Question:

Consider the circuit shown in the diagram:

        R1               R2
    ━━━━━━◦━━━━━━━━━━━━━━◦━━━━━
    ┃                            ┃
━━◦━━                      ━━◦━━━
    ┃                            ┃
    ━━━━━━━━━━━━◦━━━━━
                        ┃
                       EMF

The circuit consists of two resistors, R1 and R2, and an ideal battery with an EMF of 12V. R1 has a resistance of 4 ohms, while R2 has a resistance of 8 ohms.

a) Calculate the equivalent resistance of the circuit.

b) Determine the total current flowing through the circuit.

c) Calculate the voltage drop across each resistor.

d) Determine the power dissipated by each resistor and the total power dissipated in the circuit.

Provide all answers with detailed explanations.

Answer:

a) The equivalent resistance of the circuit can be calculated using the formula for resistors in series:

Req = R1 + R2
    = 4Ω + 8Ω
    = 12Ω

The equivalent resistance of the circuit is 12 ohms.

b) The total current flowing through the circuit can be calculated using Ohm's law:

I = V / Req
  = 12V / 12Ω
  = 1A

The total current flowing through the circuit is 1 ampere.

c) The voltage drop across each resistor can be calculated using Ohm's law:

For R1:

V1 = I * R1
   = 1A * 4Ω
   = 4V

For R2:

V2 = I * R2
   = 1A * 8Ω
   = 8V

The voltage drop across R1 is 4V, and across R2 is 8V.

d) The power dissipated by each resistor can be calculated using the formula P = I^2 * R:

For R1:

P1 = I^2 * R1
   = (1A)^2 * 4Ω
   = 4W

For R2:

P2 = I^2 * R2
   = (1A)^2 * 8Ω
   = 8W

The power dissipated by R1 is 4W, and by R2 is 8W.

The total power dissipated in the circuit can be calculated by adding the power dissipated by each resistor:

Ptotal = P1 + P2
       = 4W + 8W
       = 12W

The total power dissipated in the circuit is 12 watts.

This completes the analysis of the electric circuit.