6.1.3: Problems

Exercise \(\PageIndex{1}\): Draw the schematic diagram

\(\color{red}{\text{Bulb is unscrewed when checked, screwed in if not checked.}}\)
\(\color{red}{\text{Unscrewed bulbs are drawn in teal. Bulb color represents brightness otherwise.}}\)

You are given arrangements of identical lightbulbs with the wires connecting them hidden from view. Determine how the lightbulbs are connected by unscrewing and/or screwing the bulbs. All bulbs are initially screwed in their sockets, and the current through each bulb is given in the table (current is given in amperes). Restart.

Draw a schematic diagram representing the hidden circuit for each animation.

1. Circuit 1 - Three Bulb
2. Circuit 2 - Three Bulbs
3. Circuit 3 - Four Bulbs
4. Circuit 4 - Four Bulbs
5. Circuit 5 - Five Bulbs
6. Circuit 6 - Six Bulbs
7. Circuit 7 - Six Bulbs

Problem authored by Melissa Dancy.
Script authored by Wolfgang Christian and Melissa Dancy.

Exercise \(\PageIndex{2}\): Switched light bulbs

The circuit shown contains three lightbulbs, an ideal battery, and a variable resistor. Answer the following questions by varying the resistance and examining the current and voltage across each circuit element (voltage is given in volts, current is given in amperes, and resistance is given in ohms). Restart.

1. As you change the resistance, what happens to bulbs \(A,\: B,\) and \(C\)?
2. Why doesn't the brightness of bulb \(C\) change?
3. Why do the currents change in the way that they do?
4. Is the voltage of the battery changing? Why or why not?
5. Why do the voltages across the bulbs change the way that they do?

Problem authored by Anne J. Cox.

Exercise \(\PageIndex{3}\): Find resistance, battery voltage and power dissipated

Answer the following questions for each circuit in this animation. Assume an ideal battery (no internal resistance) and ideal meters but note that the battery and unknown resistor are different for each circuit (electric potential is given in volts and current is given in milliamperes). Use the slider to change the variable resistor. Restart.

1. What is the resistance of the unknown resistance and the voltage of the battery in each circuit?
2. What is the range of power dissipated for each circuit over the full range of variable resistance values?

Problem authored by Anne J. Cox.

Exercise \(\PageIndex{4}\): Rank resistances

Rank the three resistors (from smallest to largest) in each of the two circuits (ammeter current is given in amperes). Restart.

1. Circuit 1
2. Circuit 2

Problem authored by Anne J. Cox.

Exercise \(\PageIndex{5}\): Identify the correct graph

Assume an ideal battery. Vary the resistor and explain which of the graphs are correct and which are incorrect. Pay attention to the labels on the axes (electric potential is given in volts, current is given in amperes, resistance is given in ohms, and power is given in watts). Restart.

Problem authored by Morten Brydensholt and Anne J. Cox.

Exercise \(\PageIndex{6}\): Bad circuits

What is wrong with these circuits? Close the switches to see what happens and then explain what is wrong. Note which circuit elements are destroyed (electric potential is given in volts and resistance is given in ohms). Choose a new circuit after a circuit element is "destroyed." Restart.

1. Circuit 1
2. Circuit 2
3. Circuit 3 (Hint: What might the power rating be on the resistor?)

Problem authored by Anne J. Cox.

Exercise \(\PageIndex{7}\): Wheatstone bridge

The animation shows a "Wheatstone bridge," which is used to measure unknown resistors. Restart. Assume an ideal battery (no internal resistance) and ideal meters (resistance is given in ohms, electric potential is given in volts, and current is given in milliamperes). Begin the animation (with unknown resistor A) to read the current on the ammeter. In a Wheatstone bridge you adjust the variable resistor until the ammeter reads \(0\) and then you can calculate the value of the unknown resistor.

1. What is the unknown resistor in this case?
2. Develop an algebraic expression for the unknown resistance as a function of \(R_{1},\: R_{2}\), and the variable resistor.
3. Use your expression to quickly calculate unknown resistor B and unknown resistor C.

Problem authored by Anne J. Cox.

Exercise \(\PageIndex{8}\): Find the internal resistance of voltmeter and ammeter

Circuits \(A\) and \(B\) are different configurations of the same circuit elements. Assume the battery is ideal (no internal resistance). Restart. Pick an animation to show the voltage and current on the meters (voltage is given in volts and current is given in milliamperes).

Use circuits \(A\) and \(B\) to determine the internal resistance of the ammeter and the voltmeter that are used in both circuits. You can vary the resistor in circuits \(A\) and \(B\) (and see the resistor value).

1. Which circuit should you use to find the resistance of the ammeter? Which circuit to find the resistance of the voltmeter? Why?

Once you determine which circuit you will use to find the resistance of the ammeter, you should keep in mind the ideal resistance of an ammeter (ideally \(0\:\Omega\); why is this the ideal resistance of an ammeter?) and pick your variable resistance appropriately (e.g., if a small resistance is in series with a very large resistor, the voltage drop across the big one will not be measurably different than the voltage drop across both of them, etc.). The same is true for your determination of the resistance of a voltmeter.

2. What is the resistance of both the ammeter and the voltmeter?
3. If you don't know the internal resistance of the meters or the value of the variable resistor (which is often the case), and you simply want to divide the voltmeter reading by the ammeter reading to determine the unknown resistance, which circuit, \(A\) or \(B\), is the best for measuring small resistances?
4. Which circuit, \(A\) or \(B\), is the best for measuring large resistances? Explain.

Problem authored by Anne J. Cox.

Exercise \(\PageIndex{9}\): Find internal resistance of battery in a network

The batteries shown are not ideal (that is, they have internal resistances) but are otherwise identical. Assume ideal meters (current is given in milliamperes and voltage is given in volts). Vary the battery voltages and find the internal resistances. The internal resistance is the same for both. Restart.

Problem authored by Anne J. Cox.

Exercise \(\PageIndex{10}\): Find resistance from power graph

Assume an ideal battery. The graph shows the power dissipated by the variable resistor as a function of resistance (resistance is given in ohms and power is given in watts). Restart.

1. For Circuit A, what is the value of the unknown resistor?
2. What is the value of the power dissipated by the variable resistor when its resistance is equal to the unknown resistor?
3. Move the slider to vary the resistance. When the variable resistor is equal to the unknown resistor, how does the power dissipated by the variable resistor compare to the power dissipated when the variable resistor is not equal to the unknown resistor?
4. How can this help you find the unknown resistances in Circuit B and Circuit C?
5. What are the unknown resistances in those circuits (to within about \(10\%\))?

Problem authored by Anne J. Cox.

Exercise \(\PageIndex{11}\): RC circuit: rank the resistance of the light bulbs

In the animation, you can close and open switches to see what happens to the voltage across the capacitor \(\color{red}{\text{(red)}}\), the voltage across the resistor \(\color{green}{\text{(green)}}\), and the total voltage across the capacitor plus resistor \(\color{blue}{\text{(blue)}}\). Initially, the capacitor is charged. After pushing "play, " you should throw the switches (voltage is given in volts and time is given in seconds). Restart. Rank the resistors in the three circuits from highest to lowest and explain your rankings.

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian.

Exercise \(\PageIndex{12}\): RC circuit: find the capacitance

The graph shows the voltage across the capacitor (voltage is given in volts, resistance is given in ohms, and time is given in seconds). Initially the capacitor is charged. Find the capacitance of the capacitor. Restart.

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian and Anne J. Cox.

Exercise \(\PageIndex{13}\): RC circuit with capactor networks

The graph shows the voltage across capacitor \(A\). Run the Initial Circuit to see the voltage when there is only one capacitor (capacitor \(A\)) in the circuit. Initially the capacitor is charged, so you should open the switch (voltage is given in volts, resistance is given in ohms, and time is given in seconds). Which of the graphs, if any, correctly shows the voltage across capacitor \(A\) when there are two identical capacitors in parallel in the circuit? Restart.

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian and Anne J. Cox.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.