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 R_T = 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 : R_T = [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 I_T= V/R_T = 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.

V_T = I(R_T) = 3 (4 + 2) = 18 V.

5. Find the missing voltage.

10 W

10 W

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

???? V

V = I_TR_T , but we need R_T.

R_T = [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

I_T = 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.