Physics ab II Inductance and Circuit Page 1/5 Name: Partner: Partner: Purpose: To investigate how the voltage across an inductor changes in response to changing currents. To measure the inductance by measuring the time response of the voltage across the inductor. Equipment: oscilloscope BK function generator resistor box inductor 3 BNC to banana Background: You will investigate a circuit containing a resistor and an inductor. The function generator is the voltage source, S. It is in series with the resistor and the inductor. You will use a resistance box for the resistor. + - + S + - - Your job is to investigate how the voltage across the inductor responds when the source voltage S changes suddenly. In order to do this you will use a square wave voltage for S, while measuring. The function generator can produce the square wave (a voltage which periodically changes between two values). You will use the oscilloscope to measure so that you can see how it varies in time in response to the square wave source voltage. Here is the theory (your favorite part) picting how should vary. Kirchhoff s loop rule states that the voltage raises around a circuit equal the voltage drops. S
Physics ab II Inductance and Circuit Page 2/5 Ohm s law gives the voltage across the resistor, and the voltage across the inductor is the inductance times the time rate of change of the current. So the above equation becomes: S I di dt If S makes a sudden change to zero (as in the case of the square wave used in this lab), it turns out that the time dependence of the resulting current I(t) in the circuit is given by the solution to the equation: 0 I di dt From first semester calculus (most of you have taken this) you should recognize that the solution to this equation is the exponential function. e t So the voltage across the inductor will decay exponentially in response to sudden changes in S. ( t) 0 e t The time constant for this function is the time requi for the exponent (-t/) to equal -1. Thus for this circuit: When t = the voltage has dropped to e -1 = 0.368 (or 37%) of its initial value. You will measure how long it takes for the voltage across the inductor to drop to approximately 37% of its initial value. By using this time and the known resistance you can calculate the inductance.
Physics ab II Inductance and Circuit Page 3/5 Procedure: Examine your inductor. Estimate N, the number of turns of wire. Describe how you made your estimate. Check with your instructor and record a range for your estimate here: You will use the oscilloscope to simultaneously display the square wave source voltage S and the voltage across the inductor. On the oscilloscope make sure all three knobs are fully clockwise, in the calibrated (CA) position. Set the TIME / DI for 20 s. Set the vertical sensitivities on channels 1 (CH1) and 2 (CH2) to 1 OTS / DI. Set the MODE switch located between channels 1 and 2 to CH1. Function Generator Set up the circuit shown in the above figure. Be sure the lead from the function generator goes to the resistor box, and the lead goes to the inductor. Set the resistor box to 500. Set the function generator to produce a 10 khz square wave. Use channel 1 (CH1) on the oscilloscope to display the square wave. Plug the and leads from CH1 into the corresponding leads from the function generator. Set the oscilloscope to trigger from channel 1. (Set trigger SOUCE to INT, and MODE to AUTO. Set INT TIG to CH1.) Use the AMP knob on the function generator to adjust the amplitude of the square wave to be about 1 volt. Adjust the CH1 POSITION offset to display this signal in the upper half of the screen. Now you will use channel 2 (CH2) to measure the voltage across the inductor. Set the MODE switch located between channels 1 and 2 to AT.
Physics ab II Inductance and Circuit Page 4/5 Question: Where should you attach the CH2 leads? Adjust CH2 POSITION offset to display this signal in the lower half of the screen. Change TIME / DI to 10 s. Your oscilloscope screen should look similar to the picture below. Notice that the lower trace shows exponentially decaying curves. Measure how long it takes for the voltage to drop to 37% of its initial value. (You will not be able to do this with extreme accuracy.) Adjust the time base (TIME/ DI) and vertical scale (OTS/ DI) in order to increase the accuracy of your measurement. time to drop to 37% is Using the time that you measu, now calculate the inductance of your inductor. Show your calculation.
Physics ab II Inductance and Circuit Page 5/5 Now change your resistance to 1000 and repeat the above procedure. Show your work. Determine the average radius of the coil and the length of the coil: radius = ength = Homework 1. (A) Using the formula for inductance of a solenoid and the inductance you have measu, calculate the number of turns for the coil. 0 N 2 A Clearly show your work. (B) Does your calculated value for N seem reasonable? How well does it compare with your estimated value? 2. In the experiment you adjusted the function generator to produce a 1 volt square wave. How would your measurement of the inductance been affected if you had used a 2 volt square wave?