Consider the circuit shown in the figure below. (Assume R 1 = 12.0 , R 2 = 2.20

Question

Consider the circuit shown in the figure below. (Assume R1 = 12.0 , R2 = 2.20 , andV = 6.00 V.)

(a) Calculate the equivalent resistance of the R1 and 5.00- resistors connected in parallel. 
  

(b) Using the result of part (a), calculate the combined resistance of theR1, 5.00- and 4.00- resistors. 
  

(c) Calculate the equivalent resistance of the combined resistance found in part (b) and the parallel 3.00- resistor. 
  

(d) Combine the equivalent resistance found in part (c) with the R2 resistor. 
  

(e) Calculate the total current in the circuit. 
 A 

(f) What is the voltage drop across the R2resistor? 
 V 

(g) Subtracting the result of part (f) from the battery voltage, find the voltage across the 3.00- resistor. 
 V 

(h) Calculate the current in the 3.00-resistor. 
 A

Explanation / Answer

since R1 and 5 ohm resistor are parallel so

1/Req = 1/5 + 1/R1

1/Req = 1/5 + 1/12

a) Req = 3.5294 ohm

since 4 ohm resistor is in series with Req

so,

Req1 = Req + 4

Req1 = 3.5294 + 4

b) Req1 = 7.5294 ohm

since Req1 and 3 ohm resistor are parallel

so,

1/Req2 = 1/Req1 + 1/3

1/Req2 = 1/7.5294 + 1/3

c) Req2 = 2.14525 ohm

since Req2 and R2 are in series so,

Req3 = Req2 + R2

Req3 = 2.14525 + 2.2

d) Req3 = 4.34525 ohm

by ohm's law

V = I R

6 = I * 4.34525

I = 1.381 A

e) total current in the circuit = 1.381 A

voltage drop aross R2 = I * R2

Vdrop = 1.381 * 2.2

f) voltage drop aross R2 = 3.0382 V

voltage across the 3.00-? resistor = 6 - 3.0382

g) voltage across the 3.00-? resistor = 2.9618 V

current in the 3.00-?resistor = 2.9618 / 3

h) current in the 3.00-?resistor = 0.9873 A

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