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20 May, 06:16

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.

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  1. 20 May, 09:44
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    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
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