Which of the resistors in this circuit is using the most power? The circuit show

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Which of the resistors in this circuit is using the most power?

The circuit shown (Figure 1) is made with resistors each of which have a maximum power usage of 0.2 W. Assume the following resistor values Part A Which of the resistors in this circuit is using the most power? R2-30 R3 = 45 R1 = 5 O R R6 = 25 O R3 Figure 1 R5 Submit Hints My Answers Give Up Review Part Part B This question will be shown after you complete previous question(s). Part C R4 This question will be shown after you complete previous question(s).

Explanation / Answer

R1 and R2 are in parallel and their equivalent is in series with R3.

R12 = 5 x 30 / ( 5 + 30 ) = 4.29 Ohm

Similarly, R56 = 15 x 25 / ( 15 + 25) = 9.38

The equivalent resistance of the circuit will be:

Req = R12 + R3 + R56 + R4 = 4.29 + 45 + 9.38 + 55 = 113.67

Let Vb be the battery voltage.

I = Vb / 113.67

This current will be flowing through R12, R56 , R3 and R4 since they are in series.

So Drop across R12 is V12 = R12 x I = 4.29 x Vb / 113.67 = 0.038 Vb

V3 = R3 x I = 45 x Vb / 113.67 = 0.39 Vb

V4 = R4 x I = 55 x Vb / 113.67 = 0.48 Vb

R56 = R56 x I = 9.38 x Vb / 113.67 = 0.083 Vb

We know that P = V2/R

So, the power is proportional to the square of voltage, so high the voltage higer will be the power.

We see from the calculation that the voltage across R4 is higher than all. So it has the most power.

Hence, R4 resistor in the circuit uses the most power.

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