Four resistors are connected to a battery with a terminal voltage of 12 V, as sh

Question

Four resistors are connected to a battery with a terminal voltage of 12 V, as shown in the figure below. Use the following variables as necessary: R1 = 29.0 and R2 = 76.0 .

(a) How would you reduce the circuit to an equivalent single resistor connected to the battery? Use this procedure to find the equivalent resistance of the circuit.
=

(b) Find the current delivered by the battery to this equivalent resistance.
= A

(c) Determine the power delivered by the battery.
= W

(d) Determine the power delivered to the 50.0 resistor.
= W

Explanation / Answer

here ,

a) for the equivalent resistance ,

Req = (R1 + 50) || R2 + 20

Req = (29 + 50)|| R2 + 20

Req = 79 * 76/(76 + 79) + 20

Req = 58.7 Ohm

the net resistance is 58.7 Ohm

b)

current from the battery = V/Req

current from the battery = 12/58.7

current from the battery = 0.204 A

the current from the battery is 0.204 A

c)

Power = I^2 * Req

Power = 0.204^2 * 58.7

Power = 2.45 W

the power delivered by the battery is 2.45 W

d)

current in 50 ohm is

I1 = 76*0.204/(79 + 76)

I1 = 0.10 A

power in 50 Ohm = 0.1^2 * 50

power in 50 Ohm = 0.50 W

the power delivered to the 50.0 resistor is 0.50 W

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