RC/RL/LC Circuits | Protocol
If the voltage source is switched on at time t = 0, a time-dependent current i(t) will for the RC circuit (Equation 2 and Figure 1, where the current decreases from. In an RC circuit connected to a DC voltage source, the current decreases from . the resistance, and the capacitance of a series RC circuit in a form of equation. A sinusoidal voltage is applied to and current I flows through the resistance (R) and the capacitance The phasor diagram of the RC Series circuit is shown below If the alternating voltage applied across the circuit is given by the equation.
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. Such a time dependent current as given by Equation 2 is depicted in Figure 1.
In this case, the RC time also represents the characteristic time scale for charging the capacitor. It is the time scale for discharging a capacitor, namely, if a fully charged capacitor with voltage V is directly connected to a resistor to form a closed circuit corresponding to replacing the voltage supply in Figure 1 by a short wirethen the current flowing through the resistor will again follow Equation 2.
An analogous analysis can be made for a resistor in series of an inductor, or an "RL" circuit such as the one shown in Figure 2. However, the behavior of an inductor is opposite to that of a capacitor, in the sense that the inductor conducts better at lower frequency for steady state current the inductor acts as a short wire with little resistancebut conducts much less at higher frequency or in a transient situation because an inductor always tries to oppose the change in its current.
Equation 4 where, Equation 5 which is the general characteristic time scale for the response here the change in current of the RL circuit upon a transient change in an input here the switching on of the voltage supply. The exponential time dependence in the RC or RL circuit is related to the dissipative nature of the resistor.
Series Resistor-Capacitor Circuits | Reactance And Impedance -- Capacitive | Electronics Textbook
In contrast, an "LC" circuit where a capacitor is directly connected to an inductor with negligible resistances, such as the one shown in Figure 3a, would exhibit an oscillatory or "resonant" behavior.
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 VC 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.
In the ideal situation of no resistance and thus no dissipation in the circuit, the oscillation can go on indefinitely. In the presence of some resistance dissipationfor example in the circuit shown in Figure 3c, also known as an "RLC" circuit, such an oscillation will be damped if there is no external power supplydepicted in Figure 3d, and after a sufficient amount of time both the voltage and current would reach zero.
Diagram showing an RC circuit, with a resistor R in series with a capacitor Cconnected to a voltage supply with a switch. A representative time dependent current given by Equation 2 is depicted above the figure.
Diagram showing an RL circuit, with a resistor R in series with an inductor Lconnected to a voltage supply with a switch. A representative time dependent current given by Equation 4 is depicted above the figure.
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. Diagram showing a light bulb connected to a voltage supply with a switch. An oscilloscope is connected in parallel with the light bulb to measure its voltage proportional to the current.
Connect the inductor in series to the light bulb with the oscilloscope connected in parallel to the light bulband to the voltage supply with an open switch, as shown in Figure 5a. Observe the light bulb as well as the waveform on the oscilloscope. 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.
Diagram showing an RL circuit, with one light bulb a or two parallel light bulbs b acting as the resistor R. An oscilloscope is connected in parallel with the light bulb s to measure the voltage across the light bulb sproportional to the total current. Connect the capacitor in series with the light bulb which is connected in parallel to the oscilloscopeand 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.
Diagram showing a RC circuit, with one light bulb a or two parallel light bulbs b acting as the resistor R. 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. Diagram showing an inductor L with a switch connected in parallel to a capacitor Cwhich is part of a series RC circuit studied in Figure 6.
The oscilloscope is now connected in parallel to the inductor to measure its voltage. Resistor 'R', inductor 'L', and capacitor 'C' are fundamental circuit elements, each with different properties that are the basis of all modern electrical devices.
A resistor is an electrical component that dissipates energy, usually in the form of heat.
In contrast, a capacitor stores energy in an electric field, and an inductor stores energy in a magnetic field. When resistors, capacitors and inductors are connected together, the circuits display time and frequency dependent responses useful for AC signal processing, radios, electrical filters and many other applications.
This video will illustrate the behaviors of a resistor-capacitor and a resistor-inductor circuit, and show the oscillation in an inductor-capacitor circuit with little resistive energy loss. Let's learn how current and voltage behave in circuits involving resistors, inductors and capacitors. First, let's talk about a circuit of a resistor in series with a capacitor, called an RC circuit.
When the switch is closed, the output of the voltage source is applied across both components and current starts flowing. As, the capacitor is initially uncharged, it has zero voltage across its terminals.
- RC Series Circuit
- RC circuit
- Series Resistor-Capacitor Circuits
Hence, all of the voltage source's output appears across the resistor and the current is at its maximum value. If we look at the plot of voltage and current against time, initially VR equals source voltage the voltage across the capacitor 'VC' is zero and the current is at its max. As the current charges the capacitor, 'VC' increases. In response, VR decreases and therefore the current also goes down, in accordance with Ohm's Law.
Eventually the resistor voltage is zero and the current flow stops.
A similar analysis is possible for an RL circuit consisting of a resistor in series with an inductor. At the instant the switch closes, the sudden flow of charge creates a magnetic field in the inductor, and its voltage 'VL' is equal to the source's voltage. Consequently, the initial VR is zero and thus the initial current is also zero. Now, to monitor the changes, let's look at the voltage and current graphs like before.
Over time as the inductor voltage decreases, the voltage across the resistor increases and therefore the current also increases. Ultimately, the inductor voltage is zero, all of the voltage source output is across the resistor, and the current is at its maximum value. The decay of current and voltage transients in RC and RL circuits is caused by energy dissipation in the resistor. In contrast, an LC circuit, which has a capacitor connected to an inductor, ideally has no resistance or energy loss, and exhibits very different behavior.
The voltage across the capacitor has a phase angle of Figure below Spice circuit: However, its a simple matter to correct this figure and check to see if our work is correct. In this case, the Again, it must be emphasized that the calculated figures corresponding to real-life voltage and current measurements are those in polar form, not rectangular form!
For example, if we were to actually build this series resistor-capacitor circuit and measure voltage across the resistor, our voltmeter would indicate 1. Real instruments connected to real circuits provide indications corresponding to the vector length magnitude of the calculated figures. While the rectangular form of complex number notation is useful for performing addition and subtraction, it is a more abstract form of notation than polar, which alone has direct correspondence to true measurements.
What is RC Series Circuit? Phasor Diagram and Power Curve - Circuit Globe
Thus, the voltage phasor diagram can be replaced by a similar impedance diagram. R-C circuit Impedance phasor diagram. Find the impedance at 60 hertz. Impedances Z are managed just like resistances R in series circuit analysis: