Three resistors, r1 = 10 ω, r2 = 20 ω and r3 = 30 ω are connected in series to a 12 v battery. find: a. the equivalent resistance of the circuit. b. the current in each resistor. c. the voltage across each resistor. d. the power lost in each resistor.

Explanation:

a) The equivalent resistance for resistors in series is the sum:

R = R₁ + R₂ + R₃

R = 10 Ω + 20 Ω + 30 Ω

R = 60 Ω

b) The resistors are in series, so they have the same current.

I = V/R

I = 12 V / 60 Ω

I = 0.2 A

c) The voltage drop can be found with Ohm's law:

V₁ = I R₁ = (0.2 A) (10 Ω) = 2 V

V₂ = I R₂ = (0.2 A) (20 Ω) = 4 V

V₃ = I R₃ = (0.2 A) (30 Ω) = 6 V

d) The power lost in each resistor is current times voltage drop:

P₁ = I V₁ = (0.2 A) (2 V) = 0.4 W

P₂ = I V₂ = (0.2 A) (4 V) = 0.8 W

P₃ = I V₃ = (0.2 A) (6 V) = 1.2 W