Phys Sc 416/36

Series and Parallel: Knowing the Difference

1.                  Find the total resistance and the voltmeter reading at each resistor:

a.

50 W                A  0.50 A

40W                   30 W

Series circuit    RT = R1 + R2 + R3 = 50 + 30 + 40 = 120 W.

V1= 50(0.5) = 25 V

V2 = 15 V

V3 = 20 V

b.                                                         10 W

10 W

40 W

100 V

Parallel circuit : RT = [R1-1 + R2-1 + R3-1]-1 = [10-1 + 10-1 + 40-1]-1 = 4.4 W.

Voltage is constant, so the voltmeter would read 100 V at each resistor.

The total current would be IT= V/RT = 100/4.4 = 22.5 A

2.                  Two resistors are connected in parallel. Each draws 2.0 A of current. If the total voltage is 12 V, find R1 and R2.

R1 = V/I1 = 12/2 = 6 W.          Voltage is constant in parallel.

R2 = V/I2 = 12/2 = 6 W.

3.                  Two resistors are connected in series. The total current is 0.500 A. The potential difference at the resistors is 2 V and 5V, respectively. Find R1 and R2.

Current is constant in series.

R1 = V1/I = 2/0.500 = 4 W.

R2 = V2/I = 5/0.500 = 10 W.

4.                  Find the missing voltage and resistance.

12V

??? W               A  3.0 A

??? V

2 W

missing resistor = R1 = V1/I =12/3 = 4 W.

VT = I(RT) = 3 (4 + 2) = 18 V.

5.         Find the missing voltage.

10 W

10 W

40 W ...............................

???? V

V = ITRT , but we need RT.

RT = [R1-1 + R2-1 + R3-1]-1 = [10-1 + 10-1 + 40-1]-1 = 4.4 W.

V = 2(4.4) = 8.8 V.

6.         Find the missing resistance , the total current, and the missing voltage

10 W               1.0 A

2.0 A

????

40 W                0.25 A             ??????

???? V

V = I1R1 or I3R3 =1(10) or  0.25(40) = 10 V

IT = I1 + I2 + I3 = 1.0 + 2.0 + 0.25 = 3.25 A

7.         a.         In a series circuit, what measurement is constant at each resistor? Answer: current

b.         In a parallel circuit, what measurement is constant at each resistor? Answer: voltage.