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 = 38.0 and R2 = 79.0 .

(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 resistors are in 3 branches

1st branch has R1 and 50 ohm resistors , both of they are in series combination

Rb1 = R1 + 50 = 38 + 50 = 88 ohms

in branch 2 only 1 resistor and branch 3 also contians 1 resistor

branch 1 , 2 and 3 are in parallel combination

in parallel combination

1/Req = 1/Rb1 + 1/Rb2 + 1/Rb3

1/Req = 1/88 + 1/79 + 1/20

Req = 13.51 ohms

part b )

I = V/Req

V = 12 V

I = 12/13.51

I = 0.888 A

part c )

P = VI

P = 12 * 0.888 = 10.656 W

part d )

voltage remain same in all branches

R1 and 50 ohm in series combination so current in 1st branch

I = 12/88 = 0.136 A

current remain same in series combination

V at 50 ohm

V = IR

V = 0.0135 x 50 = 6.82 V

P = VI

P = 6.82 * 0.136 = 0.93 W

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