Professor Mason
Phys 4b
May 26 Class
Inductor Voltage and Current
The first thing in class that we learned was about Inductor Voltage and Current. An inductor is a coil of wire which stores energy in a magnetic field when it carries a current. The inductance L of an inductor is defined as the magnetic flux through the inductor per unit current. Then, we were given an equation of [L = Flux max/ i]. Any change in the current through an inductor leads to a change in the magnetic field it produces. It also will lead to a change in the magnetic flux through the inductor which, produces in induced emf in the inductor according to Faraday's Law. In the lab manual, we were given a graph of potential difference across the inductor after the switch is closed, and the voltage vs time graph is shown in the picture attached below.
The graph were measured by a tool shown in the picture above.
The moment the switch in a circuit is closed, there is no current flowing, and the voltage across the inductor is the same as the emf of the voltage source. The current starts to increase from zero, and it changes rapidly at first, and it also levels off as it reaches its steady-state value of [epsilon/R]. The potential difference across the inductor decays exponentially with the rate of change of the current as provided with an equation of [VL = E exp(-t/Time constant)], which Time constant has a formula of [Time constant = L/R] (only applies for DC circuit). The current vs time graph is shown in the picture attached below.
This picture attached above also shows us that 100 ohm resistor has the colors of Brown-Black-Brown line on it. We were also asked to calculate the value of induction of the coil if the coil has an area of 5 by 5 centimeters and also has a length of 5 cm; we calculated it using an equation of [L = Uo N^2 A/Lo], which is shown in the picture above as 4.9x10^-2 H as the answer for that calculation. We were also asked to find the value of resistance based on a copper coil of 18H (gauge) using an equation of [R = rho L/A], which is shown in the picture above as 0.3 ohm as the answer of that calculation.
Oscilloscope Experiment
Next in class, we needed to do an experiment on oscilloscope attached to a coil and a resistor in order to find the right current function graph. The steps to set up the oscilloscope are: 1. connect alligator clip from CH 1 across the output of the function generator, 2. set the function generator to produce a sinusoidal wave form, 3. set the triggering source to CH1, 4. Trigger on a positive slope, 5. adjust horizontal, vertical scale, position knobs, and triggering level knob, so it has a stable display of graph. The sketch of the circuit we needed in this experiment is shown in the picture below.
In this experiment, we needed to set up a circuit attached to an oscilloscope, and the steps are as follows: 1. measure the resistance Rl of the solenoid and R of the resistor with the DMM, 2. construct the circuit as shown above assuming that the internal resistance r of the function generator is 50 ohm, 3. connect oscilloscope in parallel with the solenoid, 4. set the function generator to produce a square wave form, 5. adjust vertical and horizontal scales and positions of the oscilloscope to display the voltage across the inductor, 6. adjust frequency of the function generator, 7. measure the half-time t_1/2 of the decay of the induced emf in the solenoid, 8. determine the inductance of the coil and its uncertainty from the measurement, 9. use measured inductance to determine the number of turns N in the solenoid and uncertainty. The graph shown in the oscilloscope based on the circuit above is shown in the picture attached below.
The calculation part of this experiment is all shown in the first picture attached at the very top of this blog; we needed to use the total R of 150 ohm because of the 100 ohm resistor added by the internal resistance of the function generator, which is 50 ohm. Then, we needed to find the period and the frequency, and they are all shown in the firs picture attached on this blog. 
The picture attached above shows us the percent error for the resistor, which is 5%; it also shows us the uncertainty for t_1/2, which is plus minus 2x10^-7 s.
Faraday's Law of Induction
Next, after we finished the oscilloscope experiment session, we continued to doing calculations on Faraday's Law of induction, which has an equation of [E = (-d Flux B/dt)N]. We were given a circuit as shown in the picture attached above, and first, we needed to calculate the time constant that has a unit of seconds shown in the picture above. Then, we also needed to calculate the voltage drop across the resistors, calculate how much time it takes from the voltage drop to exactly 11 V, calculate how much energy dissipated, calculate how much energy stored on the whiteboard using the formulas shown in the picture attached above.
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