1. Solving Problems 14.1 & 14.2

2. 1. A circuit contains 5-ohm, 3-ohm, and 8-ohm resistors in series. What is the total resistance of the circuit? Rt = R1 + R2 + R3 = 5 Ω + 3 Ω + 8 Ω Rt = 16 Ω

3. 2. A circuit contains a 9 volt battery and two identical bulbs. What is the voltage drop across each? Vt = V1 + V2; V1 = V2 Vt = 2V1 9 volts = 2V1 V1 = 4.5 volts

4. 3. A circuit contains a 12 volt battery and two 3- ohm bulbs in series. Draw a circuit diagram and use it to find the current in the circuit and the voltage drop across each bulb. Rt = R1 + R2 = 3 Ω + 3 Ω Rt = 6 Ω Since the current is the same everywhere in a series circuit: It = Vt ÷ Rt It = (12 V) ÷ (6 Ω) It = 2 amps Vt = V1 + V2; V1 = V2 12 volts = 2V1 V = 6 volts

5. 4. A circuit contains a 12 volt battery and three 1-ohm bulbs in series. Draw the circuit diagram and find the current in the circuit. Rt = R1 + R2 + R3 = 1 Ω + 1 Ω + 1 Ω Rt = 3 Ω It = Vt ÷ Rt It = (12 V) ÷ (3 Ω) It = 4 amps

6. 5. Calculate the total resistance of each circuit shown below. Then calculate the current in each. a. Rt = R1 + R2 = 1 Ω + 1 Ω Rt = 2 Ω It = Vt ÷ Rt It = (6 V) ÷ (2 Ω) It = 3 amps b. Rt = R1 + R2 = 3 Ω + 3 Ω Rt = 6 Ω It = Vt ÷ Rt It = (6 V) ÷ (6 Ω) It = 1 amps c. Rt = R1 + R2 + R3 = 1 Ω + 2 Ω + 3 Ω Rt = 6 Ω It = Vt ÷ Rt It = (12 V) ÷ (6 Ω) It = 2 amps

7. 6. A circuit contains two 1-ohm bulbs in series. The current in the circuit is 1.5 amperes. What is the voltage provided by the batteries? Rt = R1 + R2 = 1 Ω + 1 Ω Rt = 2 Ω V = It × Rt V = (1.5 A) × (2 Ω) V = 3 volts

8. 7. A circuit contains two identical resistors in series. The current is 3 amperes, and the batteries have a total voltage of 24 volts. What is the total resistance of the circuit? What is the resistance of each resistor? Rt = V/I Rt = (24 V)/(3 A) = 8 Ω R1 = R2 = Rt/2 = 8 Ω/2 = 4 Ω

9. 8. Find the amount and direction of the current through point P in each of the circuits shown below. a. 2 amps flows through point P from left to right. The current flowing from the source is 4 amps. 2 amps flows through the upper branch of the circuit and 2 amps flows through the center branch of the circuit. b. 4 amps flowing through point P from bottom to top. The sum of the current in the branches is 4 amps. c. 2 amps are flowing through point P from left to right. The sum of the current flowing back to the source is 3 amps, 1 amp from the upper branch and 2 amps from the lower branch.

10. 9. Do the following for each of the three circuits shown below. a. Find the voltage across each resistor. b. Use Ohm’s law to find the current through each resistor. c. Find the total current in the circuit. d. Find the total resistance of the circuit.

11. 10. A parallel circuit contains a 6-volt battery and two 6-ohm bulbs. a. Draw the circuit diagram for this circuit. b. Calculate the current through each branch. c. Calculate the total current. d. Use Ohm’s law to calculate the total resistance of the circuit. e. Use the formula for combining parallel resistors to calculate the total resistance of the circuit.

12. 11. A parallel circuit contains a 24 V battery, 4 Ω bulb and a 12 Ω bulb. a. Draw the circuit diagram for this circuit. b. Calculate the current through each branch. c. Calculate the total current in the circuit. d. Use Ohm’s law to calculate the total resistance of the circuit. e. Use the formula for combining parallel resistors to calculate the total resistance of the circuit.