Resistance Capacitance Circuit Investigation ✓ Solved

Resistance Capacitance Circuit Investigationname H

Resistance – Capacitance Circuit Investigation Name _________________ Hour _________ Purpose: Use this simulation to observe changes that occur in a circuit as time passes. a. Observe changes in the current during charging and discharging. b. Observe changes in the voltage across a resistor during charging and discharging. c. Observe changes in the voltage across a capacitor during charging and discharging. Procedure and questions 1. Access the PhET web site. 2. Click on Simulations. 3. From the left hand menu pick Electricity, Magnets, and Circuits. 4. Choose Circuit Construction Kit: DC & AC (Direct Current & Alternating Current) 5. Select Upload and navigate to the Teacher’s Directory to find the file I stored as R-C Circuit Simulation. It should look like the screen picture shown below. You may have to replace the red and black voltmeter connections to the proper location in the circuit. a. Charge the capacitor by closing the switch on the left. Sketch the graphs of Voltage vs. Time for the resistor and the capacitor below. b. What happens to the current through the circuit as time goes on? c. What happens to the amount of charge on the capacitor as time goes on? d. Now discharge the capacitor by opening the switch on the left and closing the switch on the right. Sketch the graphs of Voltage vs. Time for the resistor and the capacitor below. e. What happens to the current through the circuit as time goes on? f. What happens to the amount of charge on the capacitor as time goes on? g. Predict the changes to the graphs if the amount of resistance increases by drawing additional lines on your graphs above. Explain the reasons for your predictions. h. Right click on the resistor and increase the resistance. Use another color to show the results on your charging and discharging graphs above. i. Predict the changes to the graphs if the amount of capacitance increases. Use the graphs drawn below to show the original graphs and the changes that you predict. Explain the reasons for your predictions. h. Right click on the capacitor and increase the capacitance. Use another color to show the results on your charging and discharging graphs above. i. What happens to the current through the circuit as time goes on? j. What happens to the amount of charge on the capacitor as time goes on? k. What is the function of a resistor in a circuit? How does it affect the amount of charge that flows? How does it affect the rate at which charge flows? How does it affect the initial and final voltage across the capacitor? l. What is the function of a capacitor in a circuit? How does it affect the amount of charge that flows? How does it affect the rate at which charge flows? How does it affect the initial and final voltage across the resistor? How does the capacitor make charge move when there is no battery in the circuit? Purpose: How does placing more than one capacitor affect voltage drops and charge stored in a circuit? Select Upload and navigate to the Teacher’s Directory to find the file I stored as R-C Circuit Simulation II. It should look like the screen picture shown below. You may have to reconnect the voltmeter. a. Close the left hand switch to charge the capacitors. How does the voltage drop across each capacitor compare? Check the value of the batteries voltage by right clicking on it. How does the voltage drop across each capacitor compare to the voltage across the battery? Discharge the capacitors by opening the left switch and closing the right switch. Increase the capacitance of the top capacitor. Repeat the charging process. How does the voltage drop across each capacitor compare? What is the relationship between the size of the capacitor and the share of voltage it receives? Does it appear that placing two capacitors in a circuit with one pathway (series circuit) for charge increases or decreases the amount of charge stored? You may need to return to the original circuit from part I to decide. Select Upload and navigate to the Teacher’s Directory to find the file I stored as R-C Circuit Simulation III. It should look like the screen picture shown below. Check the voltmeter connections again. a. Close the bottom switch to charge the capacitors. How does the voltage drop across each capacitor compare? Check the value of the batteries voltage by right clicking on it. How does the voltage drop across each capacitor compare to the voltage across the battery? Discharge the capacitors by opening the bottom switch and closing the top switch. Increase the capacitance of the top capacitor. Repeat the charging process. How does the voltage drop across each capacitor compare? What is the relationship between the size of the capacitor and the share of voltage it receives? What is the relationship between the size of the capacitor and the amount of charge it stores? Does it appear that placing two capacitors in a circuit with multiple pathways (parallel circuit) for charge increases or decreases the amount of charge stored? You may need to return to the original circuit from part I to decide.

Sample Paper For Above instruction

The investigation of resistance and capacitance in electrical circuits provides crucial insights into the dynamic behavior of these components during charging and discharging processes. Using the PhET simulation tools, students observe how the current, voltage across resistors, and voltage across capacitors evolve over time, enhancing understanding of fundamental principles in circuit theory.

Initially, the charge process involves closing the circuit switch to allow current flow into the capacitor, resulting in observable changes in voltage and charge accumulation. As the capacitor charges, the current diminishes exponentially, approaching zero, consistent with the exponential charging curve described by the equation:

Q(t) = C * V_max(1 - e^-t/RC)

where Q(t) is the charge at time t, C is the capacitance, V_max is the maximum voltage, R is the resistance, and t is time. During this process, the voltage across the resistor starts at a maximum and decreases exponentially, while the voltage across the capacitor increases correspondingly until it equals the battery voltage.

The discharging process inversely mirrors charging; opening the charging switch and closing the discharging switch results in the capacitor releasing stored charge, decreasing both voltage and current exponentially. The current diminishes following the relation:

I(t) = (V_initial/R) * e^-t/RC

Supplanted with predictions for increased resistance and capacitance, the graphs show that higher resistance extends the time constant (τ = RC), leading to slower charging and discharging rates. Conversely, increasing capacitance results in larger stored charge and longer times to reach maximum voltage, affecting the shape and scale of the voltage vs. time graphs.

The role of resistors in circuits is to limit current flow, hence controlling the charge rate and the voltage distribution across circuit components. Conversely, capacitors store electrical energy, release it gradually, and influence the voltage dynamics across circuit elements. When multiple capacitors are arranged in series, the total voltage divides among them proportionally to their capacitance values, with smaller capacitors receiving larger voltage shares.

In parallel arrangements, the total stored charge increases since the voltage across each capacitor equals the battery voltage, and the total charge is the sum of individual charges: Q_total = C_total * V. Larger capacitance in parallel circuits stokes higher charge capacity, confirming theoretical expectations and illustrating how circuit configuration critically influences the charge storage and voltage distribution.

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