# KEY: Series Circuits (AP1)

`KEY: Series Circuits (AP1) 1. All the resistors show below are identical at 2Ω each. Batteries are 12 V ideal with voltages of either 6 V or 12 V as shown. All connecting wires have negligible resistance. a. Rank current passing through 6 V upper right hand corner of each circuit from greatest to least. Justify your ranking. Largest I C I = V / R (12/2) > B (6/2) = E (12/4) > A (12/6) > D (6/4) > Smallest I F (6/6) b. Rank voltage at upper right hand corner relative to the ground. Place highest voltage first and lowest voltage last. Justify you ranking. Think of a circuit like a mountain. The voltage is the height (12V is a higher mountain than a 6V one), resistors are obstacles on the way down, and the battery is the ski lift (it gives you height/voltage). “Ground” is at zero voltage. Highest V at upper right corner: Smallest V at upper right corner: C > A > B = E > F > D -­‐ -­‐ -­‐Note -­‐ Voltage is split equals between resistors since all the resistors are identical. C = Still at top of 12V mountain, A = Each resistor gets 4 V. After one resistor, there are 8 more volts to go. B = Still at top of 6 V mountain, E = Each resistor gets 6 V. After one resistor, there are 6 more volts to go. F = Each resistor gets 2 V. After one resistor, there are 4 more volts to go. D = Each resistor gets 3 V. After one resistor, there are 3 more volts to go. 2. A student needs a 30 Ω resistor, but all the stockroom has left is 10 Ω resistors. Can the student make a 30 Ω resistor? If so, how? If not why not? Put three 10Ω resistors in series. 3. If the multiple 10 Ω resistors from the previous problem are hooked to a 12 V battery, what is the current through each resistor and the voltage of each resistor? (0.4A; 4V) 4. A student needs a 1.0 Ω resistor, but all the stockroom has left is 4 Ω resistors. Can the student make a 1.0 Ω resistor? If so, how? If not why not? This is not possible in series. In series, the more resistors in the circuit, the larger the total resistance. (However, you could put 4 resistors in parallel; but that is for another day…) 5. A series circuit is made from a 3.0 Ω, 6.0 Ω, and 9.0 Ω resistors hooked to a 24 V battery. a. Draw the circuit b. What is the total resistance for the circuit? (18Ω) c. What is the power output of each resistor? (5.3W,11W,16W) Step 1: Calculate Itotal using Rtotal and Vtotal Step 2: Using the resistance of each resistor and the current through each resistor, calculate the power of each resistor. 6. What will the power output be when a 60 W American light bulb is plugged into a 240 V European socket (USA sockets provide 120 V)? (240W) 7. Three 75 W American-­‐made light bulbs are plugged into a circuit in series. If the circuit receives a total of 310 V, what will be the total power output of the circuit? (167W) 8. A 12 Ω and 15 Ω resistors are hooked up in series with a 9.0 V battery. What is the power dissipated by each resistor? (1.3 W; 1.7 W) Step 1: Calculate Rtotal Step 2: Calculate Itotal using Rtotal and Vtotal Step 3: Using the resistance of each resistor and the current through each resistor, calculate the power of each resistor. `