Document Sample

RC Circuits – Determining the Time Constant Purpose: To determine the time constant for an RC circuit. Background: So far we have only discussed circuits where the voltages, resistances and currents are constant. Now we will investigate RC circuits, where the voltage and currents vary with time. When a circuit with a resistor (R) and a capacitor (C) in series is closed, the capacitor is initially uncharged and so the voltage across it is equal to 0. The voltage across the resistor will be equal to the voltage of the emf. As the capacitor charges, there is an increasing electric field between the capacitor plates and therefore an increasing voltage across the capacitor. This means that the current in the circuit will decrease since the voltage across the capacitor opposes the voltage across the batteries or power supply. (You can think about this like two batteries that are put together with positive to positive – the net result will be zero volts.) Eventually, the capacitor will be very nearly fully charged and the current will effectively go to zero. Mathematically, we can describe the voltage across the capacitor by the equation VC (t) = Vo (1 – e-t/τ) Where VC is the voltage across the capacitor (in volts) Vo is the voltage across the batteries or power supply (in volts) t is the time elapsed (in seconds) τ is the time constant, RC (in seconds) Procedure: Make an RC circuit such that the batteries or power supply, the resistor and the capacitor are in series with each other but do not close the circuit until you are ready to collect data. Be ready to measure the voltage across the capacitor. Close the circuit so that the current flows and the capacitor will begin to charge. At time t = 0, the voltage across the capacitor will be zero because the capacitor has not charged up yet. Record the voltage every 30 seconds for about 10 - 15 minutes (more or less – just make sure that the voltage across the capacitor is close to the voltage across the batteries or power supply when you stop taking data). In the event that you need to start over, you can simply discharge the capacitor by running a wire from one end of the capacitor to the other and the capacitor will discharge quickly (just a second). Set up the circuit again and start over. Page 1 of 4 Data: Using the data table below or using Excel directly, make a data table that shows the following data: Voltage on power supply: Resistor value: Time (s) Voltage (resistor) (V) Voltage (capacitor) (V) 0 Page 2 of 4 Graph: Make a graph of the voltage across the capacitor versus time. Follow-Up Questions: 1. What is the value of the horizontal asymptote on your graph? What does this value signify? 2. Using the equation above for the value of the voltage across the capacitor as a function of time, find the voltage across the capacitor, VC, when t = τ. Your answer will be as a function of the voltage across the batteries or power supply. 3. What is the value of VC at t = τ for your experiment? 4. At what time is this voltage reached (use your graph)? 5. What are the units of RC? 6. What is the numerical product of RC for the resistor and capacitor that you used? Page 3 of 4 7. How is the value of RC (question 6) related to your answer from question 4? 8. If = RC where is the time constant, what does it mean to have a large or small ? How can you increase/decrease the time constant? 9. Can you think of how a small (or large) time constant might be useful in applications? Page 4 of 4

DOCUMENT INFO

Shared By:

Categories:

Tags:
RC Circuits, time constant, RC circuit, series RC circuit, capacitor voltage, the resistance, potential difference, differential equation, voltage source, Function Generator

Stats:

views: | 5 |

posted: | 4/25/2011 |

language: | English |

pages: | 4 |

OTHER DOCS BY nuhman10

How are you planning on using Docstoc?
BUSINESS
PERSONAL

Feel free to Contact Us with any questions you might have.