In this video I go over a brief introduction to some of the definitions and concepts behind electric circuit such as resistors, voltage, inductors, current, and electromotive force. The current flowing through an electric circuit can be described as a first order differential equation, which is part of Kirchhoff's Laws and also uses Ohm's law for voltage drop due to a resistor. This video is to serve as a bit of a background in order to better understand the example in my next video, which will be on describing the solution to this differential equation by using differential fields.
If you haven't learned about electric circuits, this brief overview might be useful so make to watch this video!
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Differential Equations: Direction Fields: Electric Circuit: Brief Introduction
The simple electric circuit shown below contains an electromotive force (usually a battery or generator) that produces a voltage of E(t) and a current of I(t) at time t.
- Voltage is measured in volts (V)
- Current is measured in amperes (A)
The circuit contains a resistor with a resistance of R and an inductor with an inductance of L.
- Resistance is measure in ohms (Ω)
- Ω = Greek letter omega
- Inductance is measured in henries (H)
Brief Definitions
Voltage = an electromotive force that would drive an electric current between two points
Current = a flow (or rate of flow) of electric charge
- An electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field
- This is mainly due to the difference between the number of protons and electrons.
- Excess of electrons is said to be negatively charged.
- Excess of protons is said to be positively charged
- Like charges repel
- Unlike charges attract
- In electric circuits this charge is often carried by moving electrons in a wire
- An electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field
- Resistor = an electrical component that can reduce or limit current flow and lower voltage levels, usually in the form of dissipating as heat.
- Resistors could also be the end goal of a circuit, for example, a light bulb is a resistor it involves electric resistance to create heat to make the filament in the bulb glow.
- Inductor = an electrical component that resists changes in electric current passing through it
- Basically, when current flows through an inductor a magnetic field begins to build up which resists the flow of current until the magnetic field is built up, after which the current can flow normally through.
- If the energy source is turned off, the stored up magnetic energy gets turned into electric energy and current can still flow from the inductor until it is used up.
- Thus an inductor induces an electromotive force that is always opposite to the change in current.
- i.e. turning a circuit on is the same as saying going from 0 to a current of I thus the inductor opposes this current until the magnetic field builds up.
i.e. on the other hand, turning the circuit off is the same as going from a current of I to 0 so the inductor opposes this by inducing a current until the magnetic field energy is dissipated.
- i.e. turning a circuit on is the same as saying going from 0 to a current of I thus the inductor opposes this current until the magnetic field builds up.
Ohm's Law gives the drop in voltage due to the resistor as R x I.
The voltage drop due to an inductor is L x (dI/dt).
One of Kirchhoff's Laws says that the sum of the voltage drops is equal to the supplied voltage E(t), thus we have:
which is a first-order differential equation that models the current I at time t.