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Learning Introductory Physics with Activities

Paul J. Emigh, Rebecka Tumblin, Kathryn Hadley, Danielle Skinner

Section 25.12 Practice - Circuits: Intro

Subsection Explanation Practice

Explanation 25.12.1. Circuit.

Figure 25.12.1. Circuit diagram. The top and bottom circuits are identical, apart from an extra wire connecting around lightbulb C in the bottom diagram.
The circuit shown on top in the image above has four identical light bulbs and an ideal battery.
  1. Rank the bulbs in the top circuit according to brightness, from brightest to dimmest.
    A wire is now added to the circuit, as shown in the bottom diagram.
  2. Does the brightness of bulb C increase, decrease, or remain the same?
  3. Does the brightness of bulb A increase, decrease, or remain the same?
  4. Does the current through the battery increase, decrease, or remain the same?

Subsection A*R*C*S Practice

A*R*C*S 25.12.2. Current.

The total amount of charge that has entered a wire at time t is given by:
\begin{equation*} Q(t) = Q_o (1 - e^{t/\tau}) \end{equation*}
Find an expression for the current in the wire at time \(t\text{.}\)

Subsection Numerical Practice

Calculation 25.12.3. Lightning Bolt.

A large lightning bolt had a 20,000-A current and moved 30.0 C of charge. What was its duration?
Answer.
1.50 ms

Calculation 25.12.4. How many electrons?

How many electrons flow through a point in a wire in 3.00 s if there is a constant current of I = 4.00 A?
Answer.
\(7.5 \times 10^{19}\) electrons

Calculation 25.12.5. Current.

The quantity of charge through a conductor is modeled as \(Q(t) = (4.0 \frac{\mathrm{C}}{\mathrm{s}^4}t^4 - (1.0 \frac{\mathrm{C}}{\mathrm{s}})t + 6.0 \mathrm{mC}\text{.}\) What is the current at time t = 3.0 s?
Answer.
0.431 A
Figure 25.12.2. Junction with three incoming current branches.

Calculation 25.12.6. Junction.

Can all of the currents going into the junction shown above be positive? Explain.
Answer.
No. At least one current must leave the junction, and at least one must enter the junction.
Figure 25.12.3. Current versus voltage graph.

Calculation 25.12.7. Resistance from a Graph.

Suppose you apply several different voltage differences across a circuit and measure the resulting current through the circuit; a plot of your results is shown above. What is the resistance of the circuit?
Answer.
\(1000 \ \Omega\)

Calculation 25.12.8. Bird on a Wire.

High-voltage overhead electric lines are not covered by insulation, unlike wires that are used in electric circuitry in homes. Explain why a bird that lands on a single high-voltage line does not get electrocuted.
Answer.
The bird’s feet, touching the high-voltage line, do form a complete circuit through the bird, but essentially no current flows through the bird, because the resistance value of the wire is essentially zero between the points where the bird’s feet are touching it; whereas the bird has some non-negligible resistance.
Figure 25.12.4. Circuit diagram.

Calculation 25.12.9. Circuit Quantities.

Consider the circuit above. The voltage drops across resistors 1 and 2 are 3 V and 4 V respectively.
  1. What is the voltage difference across the terminals of the battery?
  2. If the current through resistor 2 is 1.75 A, what is the current through resistor 1?
  3. Given the information from parts (a) and (b), what is the resistance of resistor 1?
Answer 1.
7 V
Answer 2.
1.75 A
Answer 3.
1.71 \(\Omega\)
Figure 25.12.5. Circuit diagram.

Calculation 25.12.10. Current Through Resistors.

Consider the circuit above.
  1. Through which resistor does the most current flow?
  2. Through which resistor does the least current flow?
Answer 1.
The most current flows through the 20 \(\Omega\) resistor.
Answer 2.
The least amount of current flows through each of the 15 \(\Omega\) resistor.

Calculation 25.12.11. Increasing Resistance.

Two identical resistors are connected in parallel across the terminals of a battery. If you increase the resistance of one of the resistors, what happens to the current through, and the voltage difference across, the other resistor?
Answer.
The current and voltage difference remain the same, if the battery is ideal.
Figure 25.12.6. Circuit diagram.

Calculation 25.12.12. Circuit Analysis.

Consider the resistive circuit shown above.
  1. Is the current going through \(R_4\) greater than, less than, or equal to the current going through \(R_1\text{?}\)
  2. Is the current going through \(R_4\) greater than, less than, or equal to the current going through \(R_2\text{?}\)
  3. What is the decrease in voltage across \(R_3\text{?}\)
  4. How much current is passing through point P?
Answer 1.
Equal to.
Answer 2.
Greater than.
Answer 3.
1.18 V
Answer 4.
0.235 A
Figure 25.12.7. Circuit diagram.

Calculation 25.12.13. Circuit Analysis II.

Consider the circuit shown above.
If \(V_A = 6 \ \mathrm{V}\text{,}\) \(V_B = 2 \ \mathrm{V}\text{,}\) \(R_1 = 4 \ \Omega\text{,}\) \(R_2 = 1 \ \Omega\text{,}\) and \(R_3 = 3 \ \Omega\text{,}\) find the magnitude of the current through resistor 1.
Answer.
0.947 A
Figure 25.12.8. Circuit segment.

Calculation 25.12.14. Circuit Segment.

What is the equivalent resistance of the circuit segment above?
Answer.
2 \(\Omega\)

Calculation 25.12.15. Parallel Resistors.

Every time you add another resistor in parallel which of the following changes occur?
  1. The voltage change across the battery increases.
  2. The voltage change across the battery decreases.
  3. The current coming through the battery increases.
  4. The current coming through the battery decreases.
  5. The total resistance of the circuit increases.
  6. The total resistance of the circuit decreases.
Answer.
(3), (6)

Calculation 25.12.16. Circuit Analysis II.

Recall the Circuit Diagram from above.
  1. What is the equivalent resistance of the circuit?
  2. How much current is passing through \(R_1\text{?}\)
  3. What is the voltage difference across \(R_4\text{?}\)
  4. If another 5 \(\Omega\) resistor were connected in parallel with \(R_2\) and \(R_3\text{,}\) would the overall resistance of the circuit increase, decrease, or stay the same?
  5. If another 5 \(\Omega\) resistor were connected in parallel with \(R_2\) and \(R_3\text{,}\) would the voltage difference across the battery increase, decrease, or stay the same?
  6. If another 5 \(\Omega\) resistor were connected in parallel with \(R_2\) and \(R_3\text{,}\) would the current drawn from the battery increase, decrease, or stay the same?
  7. If another 5 \(\Omega\) resistor were connected in parallel with \(R_2\) and \(R_3\text{,}\) would the power dissipated by \(R_4\) increase, decrease, or stay the same?
Answer 1.
25.5 \(\Omega\)
Answer 2.
0.471 A
Answer 3.
3.76 V
Answer 4.
Decrease.
Answer 5.
Stay the same.
Answer 6.
Increase.
Answer 7.
Increase.

Calculation 25.12.17. Shock!

The severity of a shock depends on the magnitude of the current through your body. Would you prefer to be in series or in parallel with a resistance, such as the heating element of a toaster, if you were shocked by it? Explain.
Answer.
It would probably be better to be in series because the current will be less than if it were in parallel.

Calculation 25.12.18. Smallest and Largest Resistances.

What are the largest and smallest resistances you can obtain by connecting a 36.0 \(\Omega\text{,}\) a 50.0 \(\Omega\text{,}\) and a 700 \(\Omega\) resistor together?
Answer.
Largest: 786 \(\Omega\text{,}\) Smallest: 20.32 \(\Omega\)

References References

[1]
Practice activities provided by BoxSand: https://boxsand.physics.oregonstate.edu/welcome.
[2]
Practice activities provided by Ling, S. J., Moebs, W., & Sanny, J. (2016). Current and Resistance, Direct-Current Circuits. In University Physics Volume 2. OpenStax.
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