Find the power dissipated in each resistor. Three resistors having resistances of R1 = 1.84 Ω , R2 = 2.28 Ω and R3 = 4.75 Ω respectively, ar

Question

Find the power dissipated in each resistor. Three resistors having resistances of R1 = 1.84 Ω , R2 = 2.28 Ω and R3 = 4.75 Ω respectively, are connected in series to a 28.5 V battery that has negligible internal resistance.Find (a) the equivalent resistance of the combination; (b) the current in each resistor; (c) the total current through the battery;(d) the voltage across each resistor; (e) the power dissipated in each resistor. (f) Which resistor dissipates the most power: the one with the greatest resistance or the least resistance? Explain why this should be.

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Thái Dương 5 years 2021-08-28T15:50:33+00:00 1 Answers 11 views 0

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  1. binhan
    0
    2021-08-28T15:52:04+00:00
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    Answer:

    a) R_eq = 8.87 Ω
    , b) i₁ = i₂ = i₃ = 3,213 A
    , c)  i = 3,213 A
    , d)   V₁ = 5,912 V,        V₂ = 7,326 V
    , V₃ = 15,262 V,  e)   P₁ = 19.0 W
    , P₂ = 23.5 W
    ,     P₃ = 49.0 W
    ,

    Explanation:

    a) and e) The power dissipated in a resistor is

         P = V I = I² R

    In a series circuit the current is constant and the equivalent resistance is the sum of the resistances

        R_eq = R₁ + R₂ + R₃

         R_eq = 1.84 + 2.28 +4.75

         R_eq = 8.87 Ω

          V = i R_eq

           i = V / R_eq

           i = 28.5 /8.87

           i = 3,213 A

    There we can calculate the power dissipated in each Resistor

            P₁ = i² R₁

            P₁ = 3,213² 1.84

            P₁ = 19.0 W

            P₂ = i² R₂

            P₂ = 3,213² 2.28

            P₂ = 23.5 W

            P₃ = i² R₃

            P₃ = 3,213² 4.75

            P₃ = 49.0 W

    b) in a series circuit the current is constant

                i₁ = i₂ = i₃ = 3,213 A

    c) The current is not lost so the current supplied by the battery must be equal to the current passing through the resistors

               i = 3,213 A

    d) V = i R

           V₁ = 3,213 1.84

          V₁ = 5,912 V

          V₂ = 3,213 2.28

          V₂ = 7,326 V

          V₃ = 3,213 4.75

          V₃ = 15,262 V

    f) the resistor that dissipates more power is the one with the highest resistance values             R₃

    E that dissipates less power is R₁

    This is because the current in a series circuit is constant through all resistors

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