You've just watched JoVE's introduction to the time dependent behavior of circuits using resistors, capacitors and inductors.
Thanks for watching! For step 1, the light bulb will "instantly" turn on and off when closing step 1. Representative oscilloscope traces are shown in Figure 8. For step 2. When two parallel light bulbs are used step 2. Representative traces on the oscilloscope for the two cases are shown in Figure 9. For step 3. When two parallel light bulbs are used step 3. Representative traces on the oscilloscope for the two cases are shown in Figure For step 4.
Some damping of the oscillation may be observed due to the finite resistance of the wires connecting the circuit. Figure 8 : Representative oscilloscope traces or "waveforms" that may be observed in the experiment depicted in Figure 4 , when the switch is closed or opened, measuring the voltage across a light bulb directly connected to a voltage supply. Figure 9 : Representative oscilloscope traces or "waveforms" that may be observed when the switch is closed in the experiment depicted in Figure 5 , measuring the voltage across a light bulb connected in series of an inductor and a voltage supply.
Figure 10 : Representative oscilloscope traces or "waveforms" that may be observed when the switch is closed in the experiment depicted in Figure 6 , measuring the voltage across a light bulb connected in series of a capacitor and a voltage supply. In this experiment, we have demonstrated the time dependent response exponential turning on and off in RC or RL circuits, and how changing the resistance affects the time constant.
We also demonstrated the oscillatory response in an LC circuit. For example, RC and RL circuits are commonly used as filters taking advantage of the fact that capacitors tend to pass high frequency signals but block low frequency signals, while the opposite is true for inductors.
They are also useful for electrical signal processing, for example, taking the derivative or integral of an electrical signal. The LC circuit is a simple example of an electrical "oscillator" or resonance circuit and is a common component in circuits used for amplifiers, radio tuning, etc. The author of the experiment acknowledges the assistance of Gary Hudson for material preparation and Chuanhsun Li for demonstrating the steps in the video. Physics II. To learn more about our GDPR policies click here.
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Login processing This is a sample clip. Sign in or start your free trial. Previous Video Next Video. Overview Source: Yong P. Log in or Start trial to access full content. The full, quantitative time-dependent current i t can be solved by: Equation 2 where, Equation 3 is known as the "RC time constant" for the "RC" circuit, and characterizes in general the time scale for the response of the RC circuit here the change in the current upon a transient change in an input here the switching on of the voltage supply.
One can show that the subsequent voltage on the capacitor same on the inductor would have the following oscillatory sinusoidal time dependence: Equation 6 where, Equation 7 is the "oscillation frequency" or "resonant frequency" here, frequency refers to the angular frequency of the LC circuit.
The current through the inductor is: Equation 8 The capacitor first discharges through the inductor V C t decreases and i t increases. The cycle repeats itself with the period in time t of, Such an oscillatory behavior, depicted in Figure 3b , also corresponds to the capacitor and inductor swapping electromagnetic energy between each other a capacitor stores energy in the electric field due to the voltage drop, and an inductor stores energy in the magnetic field due to the current.
Connect the circuit as shown in Figure 4 , with the switch open. The connections in this experiment can be made with cables, clamps, or banana plugs into receiving ports on the instruments. Select the vertical scale of the oscilloscope to a range that is close to 1 V. Select the time scale of the oscilloscope to a range that is close to 1 s.
Close the switch thus switching on the light bulb. Observe the light bulb as well as the trace "waveform" on the oscilloscope screen. The oscilloscope, connected in parallel to the light bulb, will measure the voltage across the light bulb, and this voltage is proportional to the current through the light bulb. Now open the switch again thus switching off the light bulb. Again observe the light bulb as well as the trace "waveform" on the oscilloscope screen.
Repeat the steps 1. Connect the inductor in series to the light bulb with the oscilloscope connected in parallel to the light bulb , and to the voltage supply with an open switch, as shown in Figure 5a. Close the switch. Observe the light bulb as well as the waveform on the oscilloscope. Open the switch. Obtain another light bulb of the same kind as the first light bulb and connect it in parallel with the first light bulb, as shown in Figure 5b.
Repeat step 2. Connect the capacitor in series with the light bulb which is connected in parallel to the oscilloscope , and together to the voltage supply with the open switch, as shown in Figure 6a. This corresponds to the similar circuit shown in Figure 5a connected in step 2. Connect the second light bulb in parallel with the first light bulb, as shown in Figure 6b.
Repeat step 3. Close the switch 1 to have the capacitor charged. No light bulbs are used in this part of experiment. Connect the oscilloscope in parallel with the capacitor, as shown in Figure 7. Now open switch 1, then right away also close switch 2. Observe the oscilloscope.
Close the switch to apply power to the light bulb. Please enter your institutional email to check if you have access to this content. Please create an account to get access. Forgot Password?
Please enter your email address so we may send you a link to reset your password. Notice that inductance is now based on the coil's geometry: the total number of loops, its total length, and its cross-sectional area. Another expression used to describe the electric fields between the plates of the capacitor is the electric field energy density, u E.
Another expression used to describe the magnetic field established within the coils of the solenoid, or inductor, is the magnetic field energy density, u B. If we look at the graph for charging a capacitor we see that the uncharged capacitor initially acts as if it has "0" resistance to the flow of current.
But as charge grows on its plates, it restricts the placement of additional charge the voltage is fast approaching is maximum value and the current stops.
If we look at the corresponding graph for an inductor when the switch is initially closed and current starts flowing through the circuit, we see that the inductor acts like it has "infinite" resistance since it opposes Lenz' Law any changes in the flux within its coils. The formula presented for the instantaneous current in the circuit includes a factor called the "RC time constant. Mathematically this is necessary since e x must be a dimensionless value.
Substituting in all values yields a final unit of seconds. Our graph shows us that after on time contant, the current will have grown by 1 - 0. Once the currents in the circuit reach steady-state conditions, the capacitor is completely charged and behaves like a resistor with "infinite" resistance.
It is clear from the above diagram that the charge increases with the increase in voltage. In order to understand capacitance, we need to analyze the diagram above.
The slope of the above graph represents the value of capacitance. The area covered in the above graph represents the energy stored in the form of the electric field. This is because the parallel plates of the capacitor store the charge and it gets converted into electrostatic energy.
The energy stored in form of the electric field can be written in terms of charge and voltage. With the help of below equation, you can develop a better understanding of RC circuit. The RL circuit consists of resistance and inductance connected in series with a battery source. The current from the voltage source experiences infinite resistance initially when the switch is closed.
As soon as the RL circuit reaches to steady state, the resistance offered by inductor coil begins to decrease and at a point, the value of resistance of RL circuit becomes zero. The flux linking with the inductor coil creates the magnetic field around it.
Moreover, the flux varies with the current flowing through the coil. The variation of flux with the current is shown below with the help of a graph. The slope of the graph depicts the value of inductance while the area covered by the graph determines the energy stored in the form of magnetic field. To understand it more clearly, you may refer to the equation shown below.
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