Three resistors, each of different value, are used in a circuit with a power source supplying 12 volts. For which of the following resistor

Question

Three resistors, each of different value, are used in a circuit with a power source supplying 12 volts. For which of the following resistor combinations is the total power supplied the greatest?

a. all three resistors in parallel
b. two of the resistors in parallel with the third resistor in series with the parallel pair
c. This cannot be found until it is known which resistor is in series with the parallel pair.

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Thiên Thanh 4 years 2021-08-27T07:15:03+00:00 1 Answers 28 views 0

Answers ( )

  1. kiet
    0
    2021-08-27T07:16:06+00:00
    Reply

    Answer:

    a. all three resistors in parallel

    Explanation:

    Combination of Resistors

    The power supplied by a power source or V volts is:

    \displaystyle P=\frac{V^2}{R}

    where R is the equivalent resistance of the whole circuit connected to the power source.

    As shown, the power is inversely proportional to R which means that if R is a minimum, P is a maximum.

    The problem reduces now to find the combination of resistors that produces the least value of its equivalent. If three resistors are connected in series, the equivalent is the sum of all them

    R=R_1+R_2+R_3

    This equation gives R a value that is greater than the greatest of all three resistances.

    If they are connected in parallel, the equivalent is given by

    \displaystyle \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}

    This equation produces for R a value that is smaller than the smallest value from the three resistances.

    Any other combination of resistors will produce intermediate values between the maximum (series) and the minimum (parallel), thus:

    a. all three resistors in parallel

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