Name ______________________ Box # ____________
Score ____ / 20 Date ___________
AP Physics – Worksheet #4: Chapter 19
Resistors in Series and Parallel
Purpose: To develop an understanding of calculating resistor combinations in series and parallel,
and the use of Ohm’s Law: V = IR and the Power equation: P = IV. For resistors in series,
resistance adds: R = R1 + R2; for resistors in parallel, inverse resistance adds: 1/R = 1/R1 + 1/R2.
Given the three resistor system shown to the right, determine the current flowing across each
resistor, the voltage drop across each resistor, and the power dissipated by each resistor by
performing the following calculations.
1. Determine the equivalent resistance Rp due to the 3 Ω and
6 Ω resistors in parallel.
Rp = ____________
Step1: Resistors in parallel
2. Determine the equivalent resistance Rs due to the 4 Ω and
Rp resistors in series.
Rs = ____________
Step 2: Resistors in series
3. Now that the total equivalent resistance of the system is
determined, find the total current in the system using V = IR.
Itotal = ____________
4. Determine the total power dissipated in the system using
P = IV.
Steps 3 and 4: Finding total
current and power dissipated
Ptotal = ____________
5. Knowing that the current is constant and equal to Itotal
through resistors in series, determine the potential drop ΔV
across the two resistors 4 Ω and Rp in series using the equation
V = IR.
ΔV4 = ____________
Step 5: Resistors in series
ΔVp = ____________
As a check, ΔV4 + ΔVp should equal the total voltage applied
by the battery: 12 V. Confirm this.
ΔV4 + ΔVp = ____________
6. Knowing that the voltage is constant and equal to ΔVp
through resistors in parallel, determine the current flowing
across the parallel resistors 3 Ω and 6 Ω using the equation V
= IR.
Step 6: Resistors in parallel
I3 = ____________
I6 = ____________
As a check, I3 + I6 should equal the total current, Itotal.
Confirm this.
Step 7: Complete system
I3 + I6 = ____________
7. You now have all the information needed to fill in the following table. Calculate the power
dissipated across each resistor using the equation P = IV.
Resistance (Ohms)
Potential drop (Volts)
Current (Amps)
Power (Watts)
4Ω
3Ω
6Ω
As a check, the sum of the power dissipated across each resistor should equal the total power
calculated in step 4, Ptotal. Confirm this.
P2 + P3 + P6 = ____________
8. Repeat the previous process with the following system and fill in the table at the bottom:
Resistance (Ohms)
Potential drop (Volts)
Current (Amps)
Power (Watts)
R1 = 2 Ω
R2 = 4 Ω
R3 = 3 Ω
Reff =
Vtotal =
Itotal =
Ptotal =