CHARGE - q(t)
Electric charge is the most basic quantity in an electric circuit.
Charge is defined as electrical property of the atomic particles of which matter consist. It exist as a negative (electron) and positive (proton) charges. Charge is measured in Coulomb (C).
The coulomb is a large unit for charges. In 1 C of charge, there are
1/(1.602x10^-19) = 6.24x10^18 electrons.
The law of conservation of charge states that charge can neither be created nor destroyed, only transferred. Thus the algebraic sum of the electric charges in a system does not change, where it can be converted to another form of energy.
CURRENT - i(t)
Electric current is the movement of charged particles in a specific direction. The charged particle may be an electron, a positive ion or a negative ion, and they are referred to as current carriers.
Electric current is the time rate of change of charge, the symbol used for current is I, and the unit is given in coulomb per second (C/s). It was named ampere (A) after the French physicist Andre Marie Ampere (1775-1836), who discovered that two parallel wires attract each other when currents flow through them in the same direction and repel each other when currents are made flow in opposite directions.
Mathematically, the relationship between
current i, charge q, and time t is:
current i, charge q, and time t is:
The charge transferred between time to and t is obtained by integrating both sides of equation 1.
If the current does not change with time, but remains constant, we call it a direct current (dc). By convention the symbol I is used to represent such a constant current.
A time varying current is represented by i. A common form of time-varying current is the sinusoidal current or alternating current (ac)
A time varying current is represented by i. A common form of time-varying current is the sinusoidal current or alternating current (ac)
VOLTAGE - v(t)
To move the electron in a conductor in a particular direction requires some work or energy transfer, This work is performed by an external electromotive force (emf), typically represented by the battery, This emf is also known as voltage or potential difference.
The voltage vab between two points a and b in an electric circuit is the energy (or work) needed to move a unit charge from a to b; mathematically,
Voltage is the energy required to move a unit charge through an element.
POWER - p(t) and ENERGY
Power defined to be the time rate of doing work.
Measured in watts (W)
Power can be absorbed or supplied by circuit elements.
p here is a time-varying quantity and is called instantaneous power.
Power can be absorbed or supplied by circuit elements.
positive power: element that absorbs power
negative power: element that supplies power
An ideal circuit is: ∑Psupplied + ∑Pabsorbed =0
(derived form the Law of Conservation of energy.)
Energy is the capacity to do work, measured in Joules (J)
Power can be absorbed or supplied by circuit elements.
positive power: element that absorbs power
negative power: element that supplies power
An ideal circuit is: ∑Psupplied + ∑Pabsorbed =0
(derived form the Law of Conservation of energy.)
Energy is the capacity to do work, measured in Joules (J)
CIRCUIT ELEMENTS AND SOURCE
An element is the basic building block of a circuit. An electric circuit is simply an interconnection of the elements.
There are two types of elements found in electric circuit:
1. passive elements - elements that absorb energy
(i.e: resistors , capacitors and inductors)
2. active elements - elements that capable of generating energy.
(i.e: batteries, generators)
The most important active elements are voltage and current sources that generally deliver power to the circuit connected to them.
There are two kinds of Sources:
1. independent source - is an active element that provides a specified voltage or current that is completely independent of other circuit elements.
2. dependent source or controlled source - is an active element in which the source quantity is controlled by another voltage or current.
There are two types of elements found in electric circuit:
1. passive elements - elements that absorb energy
(i.e: resistors , capacitors and inductors)
2. active elements - elements that capable of generating energy.
(i.e: batteries, generators)
The most important active elements are voltage and current sources that generally deliver power to the circuit connected to them.
There are two kinds of Sources:
1. independent source - is an active element that provides a specified voltage or current that is completely independent of other circuit elements.
2. dependent source or controlled source - is an active element in which the source quantity is controlled by another voltage or current.
FIGURE 1
In the figure 1 (a) and (b) can be used to represent a dc voltage source, but only the symbol in figure 1 (a) can be used for a time-varying voltage source. An ideal independent current source is an active element that provides a specified current completely independent of the voltage across the source. That is, the current source delivers to the circuit whatever voltage is necessary to maintain the designated current.
FIGURE 2
The symbol for an independent source is displayed in figure 2, where the arrow indicates the direction of current i.
FIGURE 3
Dependent sources are usually designated by diamond-shaped symbols, as shown in figure 3. Since the control of the dependent source is achieved by a voltage or current of some other element in the circuit, and the source can be voltage or current.
Four possible types of dependent sources:
1. a voltage-controlled voltage source (VCVS)
2. a current-controlled voltage source (CCVS)
3. a voltage-controlled current source (VCCS)
4. a current-controlled current source (CCCS)
Four possible types of dependent sources:
1. a voltage-controlled voltage source (VCVS)
2. a current-controlled voltage source (CCVS)
3. a voltage-controlled current source (VCCS)
4. a current-controlled current source (CCCS)