Question

Use the exact values you enter to make later calculations The figure below shows a battery connected to a circuit. The potential difference across the battery and the resistance of each resistor is given in the figure. (Assume R. - 12.00 R - 2.500, and V- .00 ) W 4.000 M 5.000 (a) What is the equivalent resistance (in) of R, and the 5.00 resistor?

Answer 1

Remember:
For series combination
Req = R1 + R2 + R3 +...............
for parallel combination
1/Req = 1/R1 + 1/R2 + 1/R3 + ............
for 2 resistors in parallel it will be
Req = R1*R2/(R1+R2)
Using this Information:

R1 = 12.0 ohm, R2 = 2.50 ohm, R3 = 3.00 ohm, R4 = 4.00 ohm & R5 = 5.00 ohm

Part A.

R1 and R5 are in parallel, So

R15 = 12.0*5.00/(12.0 + 5.00)

R15 = 3.53 ohm

Part B.

R15 and R4 are in series, So

R145 = R15 + R4 = 3.53 + 4.00

R145 = 7.53 ohm

Part C.

R145 and R3 are in parallel, So

R1345 = Rp = 7.53*3.00/(7.53 + 3.00)

Rp = 2.15 ohm

Part D.

Now Rp and R2 are in series, So

Req = Rp + R2 = 2.15 + 2.50

Req = 4.65 ohm

Part E.

Using ohm's law:

V = Ieq*Req

Ieq = V/Req = 6.00/4.65

Ieq = 1.29 Amp

Part F.

Now remember in resistors parallel combination voltage distribution in each part will be same and in series combination current distribution in each resistor will be same. Since R2 and Rp are in series, So

I2 = Ip = Ieq

I2 = Current in R2 = 1.29 Amp

V2 = Voltage drop across R2 = I2*R2

V2 = 1.29*2.50

V2 = 3.23 V

Part G.

Ip = 1.29 Amp

Vp = Ip*Rp

Vp = 1.29*2.15 = 2.77 V

Now since R145 and R3 are in parallel, So

V3 = V145 = Vp

V3 = Voltage drop across R3 resistor = 2.77 V

Part H.

Using ohm's law:

V3 = I3*R3

I3 = V3/R3 = 2.77/3.00

I3 = 0.923 Amp = Current in R3 resistor

Let me know if you've any query.