The drawing shows the same three different resistors wired in series and then pa

Question

The drawing shows the same three different resistors wired in series and then parallel to the same battery. The resistors have resistances of R_1 = 50 Ohm, R_2 = 25 Ohm and R_3 = 10 Ohm and the battery voltage is 26 V. Pick either one of the two circuits and calculate the (a) current in, (b) voltage across and (c) power consumption of each resistor and also (d) the total power provided to the circuit by the battery. (Your solution should clearly describe which of the two circuits you chose. You may choose to do both if you wish, but if you do your recorded grade for this question will be for the circuit you make the most mistakes on.) you make the most mistakes on)

Explanation / Answer

consider circuit b )

Since the battery Voltage is in parallel to each of the three resistors, hence the Voltage across each resistor will be same as the battery Voltage

hence V = V1 = V2 = V3 = 26 Volts

a)

i1 = current in resistor R1 = V1/R1 = 26/50 = 0.52 A

i2 = current in resistor R2 = V2/R2 = 26/25 = 1.04 A

i3 = current in resistor R3 = V3/R3 = 26/10 = 2.6 A

b)

Since the battery Voltage is in parallel to each of the three resistors, hence the Voltage across each resistor will be same as the battery Voltage

hence V = V1 = V2 = V3 = 26 Volts

c)

P1 = power consumption across R1 = V12/R1 = (26)2/50 = 13.52 Watt

P2 = power consumption across R2 = V22/R2 = (26)2/25 = 27.04 Watt

P3 = power consumption across R3 = V32/R3 = (26)2/10 = 67.6 Watt

d)

equivalent resistance of the parallel combination of the resistances is

1/R = 1/R1 + 1/R2 + 1/R3

1/R = 1/50 + 1/25 + 1/10

R = 6.25 ohm

power provided by the battery is given as

P = V2/R = 262/6.25 = 108.2 Watt

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