Activity 1
Batteries have been important for a long time, and their importance is only increasing due to, for example, electric cars, unmanned aircraft systems, and the growth of portable devices. Imagine that a battery is connected to a load (any device that consumes power, e.g., an external resistor) and the voltage across the battery is measured with a voltmeter. Will the battery voltage change if the value of the external resistor is changed? Make a prediction (e.g., yes or no) and jot down the reason(s) for your prediction.
Activity 2
https://phet.colorado.edu/sims/html/circuit-construction-kit-dc-virtual-lab/latest/circuit-construction-kit-dc-virtual-lab_all.html
1. Take a few minutes to play with the circuit simulator to familiarize yourself with the controls. For practice, try dragging a battery, six wires, and a lightbulb onto the simulation desktop, connect them all in one series circuit (i.e., a loop) and see the lightbulb light up. Afterward, clear off the circuit desktop by selecting each circuit element (it will highlight in yellow), and deleting the circuit element by selecting the trash can. You should end up with a blank circuit desktop as when you started the circuit simulation. The following video is a quick start guide for the circuit simulator.
2. This time, drag a battery, five wires, an ammeter, and a resistor onto the circuit desktop and connect them all in one series circuit (i.e., a single loop). You should observe a simulated current flow.
3.Drag a voltmeter onto the circuit desktop and connect one probe to each side of the battery. You should observe that a battery voltage is displayed on the voltmeter. Select the battery and set its voltage to 9 volts.
4.Note that to measure current, it was necessary to make the ammeter part of the circuit, while measuring voltage was simply done by measuring across the battery without opening the circuit. This reflects the fact that current is a “through” variable (that measures a flow) and voltage is an “across” variable (that measures a difference). Hence, voltmeter measurements are easier to make than ammeter measurements, where the circuit has to be opened to measure the current. (Note that some ammeters, “clamp meters,” can indirectly measure currents due to the magnetic fields created by the current flow and do not require opening a circuit. However, they are generally limited to larger currents and are less precise than in-circuit ammeters).
5.Select the Advanced option and move the battery resistance slider to midway (5 ohms). Did the battery voltage change just by adding internal resistance to the battery (i.e., without even changing the value of the external resistance)? Is this result consistent with your prediction? What do you suppose is the source of a battery’s internal resistance, i.e., do you think there is a resistor inserted in the battery, or is the battery’s internal resistance due to something else?
6.Select the external resistor and move the resistance slider to various values and observe the battery voltage. Are these results consistent with your initial prediction? When is the battery voltage lowest (e.g., for the highest or lowest values of the external resistor)? How do you explain these results?
Activity 3.
Instead of viewing a battery as an “ideal” battery with a fixed voltage (which is tempting because of the voltage labeled on the sides of many batteries), we will develop a “realistic” battery model. This involves viewing a battery as an internal voltage (usually called an EMF, an acronym for electromotive force, denoted by a script E, ℰ) and an internal resistance (due to the chemical reaction in the battery), represented by a lower-case r. We can’t directly measure ℰ or r as these are inside the battery. All we can directly measure at the terminals of the battery is the terminal voltage, VT.
The following is a schematic diagram of a realistic battery model connected in a circuit to an external resistor R.
Battery circuit 3
A schematic diagram of a realistic battery model connected in a circuit to an external resistor R.
Let’s work out an equation that describes how the battery behaves in the circuit. To accomplish this, we’ll use Ohm’s law and a new idea. The new idea is that if we start at any point in the circuit and add all the voltage differences around the loop and return to our starting point, the sum of all the voltage differences will be 0. This can be viewed as a consequence of energy conservation. Alternatively, by viewing voltage as analogous to elevation, if you start somewhere and walk in a loop, going up or down in elevation, you will return to exactly the same elevation you started at, i.e., all the differences in elevation will sum to zero.
Note that the arrows in the circuit show the direction of current flow (current flows from positive to negative), and the polarities (+ and -) on the resistors reflect this (i.e., a current that enters a resistor is positive and a current that leaves a resistor is negative). The polarity of the battery terminals is determined by the battery terminals themselves (in the symbol for a battery in a schematic diagram, the longer line is positive, and the shorter line is negative).
Now let’s add up all the voltage differences around the circuit loop and set them equal to zero. Start at a point, say, just below the battery, and going clockwise around the loop, write down all of the voltage differences using Ohm’s law as follows:
– Ir + ℰ – IR = 0
Note that the minus (-) sign in front of Ir is because in going clockwise around the loop, the voltage went from + to – across internal resistance r, so the change was negative.
Since the voltage (IR) across the external resistor R is the same as the terminal voltage VT (they are connected together), IR can be replaced by VT in the equation. The battery equation now becomes:
– Ir + ℰ – VT = 0
Solving for the battery terminal voltage (the easiest property of the battery to measure, requiring only a voltmeter) gives:
VT = ℰ – Ir
The Battery Equation
This equation (in bold) is the battery equation that can be used to explain many observations about how batteries work in circuits!
VT is the terminal voltage that a voltmeter measures when connected across the battery.
ℰ is the voltage of the internal cell(s) of the battery and roughly equals the voltage labeled on the battery and does not change.
r is the value of the battery’s internal resistance (a “good” battery generally has a lower internal resistance than a “bad” battery).
I is the current in the circuit.
Observations to be discussed in your Module 8 Experiment Report (on the next Canvas page).
Using the battery equation, explain why a battery’s terminal voltage decreases when the external load resistance it is connected to decreases.
A car won’t start. The car owner connects a voltmeter across the battery terminals, and the voltmeter reads 12 volts, just like a “good” battery. However, when the car is taken to an auto repair shop, their voltage test shows the battery voltage has dropped well below 12 volts, and they correctly conclude the battery is “bad.” Using the battery equation, discuss what must have been different about the battery test performed at the auto shop.