Objective
This experiment demonstrates: a) the relationship between voltage, currrent, and resistance in an electrical circuit [Ohm's Law, which states that Voltage (volts) = Current (amperes) x Resistance (ohms)] and b) the difference between series and parallel circuits.

Equipment
See the Java applets below.

Definition

• Ohm's law: V = IR
• Power: P = VI = I²R
• R_series = R₁ + R₂
• 1/R_parallel = 1/R₁ + 1/R₂
• Also, please review the waterfall and "fork-in-the-road" analogies for serial and parallel circuits outlined in the lecture notes for Chapter 7
  • If you're confused about what the voltage drop across a resistor is, think in terms of the waterfall analogy again. The battery is like a pump that raises the water from the zero-level to the maximum height (e.g., a 9-V battery raises charges from 0-V to 9-V). Then, if you had a single resistor in a circuit, the voltage drop across that resistor is from 9-V to 0-V (this is like the water pump lifting a packet of water up to a 9-m height and the resistor is like the waterfall where the packet of water drops back down from 9-m to 0-m). The current, whether the water current or charge flow, is still the same everywhere in the river (or the circuit).

Procedure

Part A: Series Circuit

URL: http://ww2.unime.it/dipart/i_fismed/wbt/ita/kim/resistenze/serie_ita.htm

1. Click the radio button for the first resistor, R1, and set the battery's Voltage to 5-V (the circuit should now contain only a single resistor, R1). Close the switch to activate the circuit.
2. What is the Voltage across the resistor, R1? What is the current flowing through the circuit, as measured by the Ammeter?
3. Now increase the voltage in 1-V increments to the maximum (15-V) and record the current measurements for each point.

   VoltageBattery [V]	VoltageR1 [V]	Current, I [Amps]
   5-V
   6-V
   7-V
   8-V
   9-V
   10-V
   11-V
   12-V
   13-V
   14-V
   15-V

4. Make a Voltage vs. Current (V vs. I) plot and find the value of the resistance for the resistor R1 from this graph (don't forget to use proper units and label the axes of your graph).

   Graph of Voltage (V) vs. Current (I)

   Slope [V/Amps]	Resistance, R1 [Ω]

5. Set the battery's voltage back to 5-V and choose the radio button corresponding to the 2^nd resistor, R2 (the circuit should now contain only a single resistor, R2).
6. Close the switch and record both the voltage across the resistor R2 and the current shown on the Ammeter. Using these values and Ohm's law, what is the resistance of the resistor, R2?

   VoltageBattery [V]	Current, I [Amps]	Resistance, Rw [Ω]
   5-V

7. Now choose the third radio button, the one corresponding to the two resistors in series (the circuit should now contain both resistors, R1 and R2, in series).
8. Set the battery's voltage to 9-V. BEFORE closing the switch, predict what the current in the circuit should be (i.e., find I_Total using Ohm's law and the fact that your V_Total = V_Battery and that R_Total = R₁ + R₂). Record your hypothesis below.

   VoltageBattery [V]	Resistance, RTotal [Ω]	Current, ITotal [Amps]
   9-V

9. Now close the switch and test your hypothesis. Were you right? What was the reason for the discrepancy, if any?
10. What is the power rating for each resistor (in series) at 9-V?

    VoltageBattery [V]	Power, PR1 [Watts]	Power, PR2 [Watts]
    9-V

11. Now set the battery to 12-V, record the current, and calculate the power rating for each resistor (in series) at 12-V.

    VoltageBattery [V]	Power, PR1 [Watts]	Power, PR2 [Watts]
    12-V

12. Is it the same? What does this imply about the power output of regular light bulbs that you use at home (with a household voltage of 120V) when you plug them to a 12-V car batter, for example?
13. Suppose the resistors were actually bulbs. What would happen to the current and voltage (as measured by the Voltmeter and Ammeter, respectively) if the 2^nd bulb (or resistor R2) suddenly went out?

The Java Applet:

• This applet shows the essentials of a simple series circuit with two resistors of fixed value by connecting them in series (the two resistors can also be inserted independently). The Voltage (or EMF) of the battery can be varied and, as a result, the Voltmeter (which is in parallel on the resistor) and the Ammeter (which is connected in series in the circuit) will show the varying values.
• The switch can be opened or closed by clicking on it with the mouse.
• You can change the Voltage of the battery from 5.0 V to 15.0 V by clicking on the scroll bar.
• The maximum for the Ammeter is 10.0 A; that for the Voltmeter is 20.0 V
• Click on one of the radio buttons in the top, blue square on the right to select either the first Resistor (R1), the second resistor (R2), or both resistors (R1 & R2).
• If the combination of the Voltage-value and the Current-value, as calculated via Ohm's law) comes in too great, a warning message is issued that the instrument has measured a value that's out of its scale (the value is shown in red). If, under these conditions, the value is not brought back under normal operation levels by varying the Voltage, the switch is opened automatically.
• Remember, the Voltmeter is in parallel across the resistor and the Ammeter is in series with the resistor.

• Ohm's law
• The basics of electrical circuits
• Connecting resistors in series

• Using Ohm's law, calculate the values of R1, R2, and R1+R2
• Using Ohm's law, calculate the current and verify
• Vary the Voltage and verify its values using the calculated resistances and the current measred via the Ammeter

Part B: Parallel Circuit

URL: http://ww2.unime.it/dipart/i_fismed/wbt/ita/kim/resistenze/parallel_ita.htm

1. Click the 3^rd radio button so that your circuit contains both resistors, R1 and R2, in parallel with each other. Set the battery's voltage to 9-V.
2. Now close the switch and record the voltage across each resistor, the current in each of the three circuit paths, and the total voltage across both resistors together.

   Voltage VBattery [V]	Voltage VR1 [V]	Voltage VR2 [V]	Current I1 [A]	Current I2 [A]	Current ITotal [A]	Voltage VTotal [V]
   9-V

3. How does the total current flowing through the whole circuit when the resistors are in parallel compare to the total current when the resistors were in series? What does that mean about the power dissipated across each resistor/bulb? Are the bulbs brighter in series or in parallel?
4. Compute the total resistance of the parallel circuit using 1/R_parallel = 1/R₁ + 1/R₂. How does this compare to the total resistance of the series circuit above?

   Resistance, RTotal [Ω]

5. Suppose the resistors were actually bulbs. What would happen to the current and voltage (as measured by the Voltmeter and Ammeter, respectively) if the 2^nd bulb (or resistor R2) suddenly went out?

The Java Applet:

• This applet shows the essentials of a simple parallel circuit with two resistors of fixed value by connecting them in parallel (the two resistors can also be inserted independently). The Voltage (or EMF) of the battery can be varied and, as a result, the Voltmeter (which is in parallel on the resistor) and the Ammeter (which is connected in series in the circuit) will show the varying values.
• The switch can be opened or closed by clicking on it with the mouse.
• You can change the Voltage of the battery from 5.0 V to 11.0 V by clicking on the scroll bar.
• The maximum for the Ammeter is 10.0 A; that for the Voltmeter is 20.0 V
• Click on one of the radio buttons in the top, blue square on the right to select either the first Resistor (R1), the second resistor (R2), or both resistors (R1 & R2).
• If the combination of the Voltage-value and the Current-value, as calculated via Ohm's law) comes in too great, a warning message is issued that the instrument has measured a value that's out of its scale (the value is shown in red). If, under these conditions, the value is not brought back under normal operation levels by varying the Voltage, the switch is opened automatically.
• Remember, the Voltmeter is in parallel across the resistor and the Ammeter is in series with the resistor.

• Ohm's law
• The basics of electrical circuits
• Connecting resistors in parallel

• Using Ohm's law, calculate the values of R1, R2, and R1+R2
• Using Ohm's law, calculate the current and verify
• Vary the Voltage and verify its values using the calculated resistances and the current measred via the Ammeter

Questions

• See the last few items in the procedure for the questions

Notes

• Some program notes:
• Be sure to use the correct units for each measurement and calculation!
• Record all data directly into your lab notebook