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.

The study of matter is called physics.

The correct answer is A.

To calculate the voltage supply in the circuit is as follows:-

where

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

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

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),

Hence, the correct answer is A that is all three resistors in parallel.

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a. all three resistors in parallel

Explanation:

Combination of Resistors

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

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

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

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