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circuit-theory

# circuit-theory - Circuit Variables Scientific investigation...

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Circuit Variables Scientific investigation of static electricity was done in late 1700’s and Coulomb is credited with most of the discoveries. He found that electric charges have two attributes: amount and polarity. There are two type of charges – opposite charges attract and similar polarity ones repel each other. Charge polarity is indicated by positive and negative signs because positive and negative charges cancel each other when brought together. As a results, the electric charge can be described by an algebraic number, q , with units of Coulomb (C). Because opposite charges attract each other, energy is expanded to separate them from each other. This energy is stored in the electric field between the two “reservoir” of separated charges and is recovered when the charges are allowed to come together. The stored energy per unit charge is called the “voltage” or potential di ff erence between the two reservoir of charges: v = dW dq Unit: volt (V = J/C) Note that we need two reservoir of charges. So voltage is between two points. We also use + and - signs to indicate the direction for measuring v . From definition of voltage above, w is energy needed to move a positive charge from - reservoir to + reservoir. One can define a reference point for measuring voltages (typically shown as ground). The voltage between any point and this reference point is call the potential of that point. It is always assumed that + is at the point and the - sign is at the reference point. Therefore, there is no need to indicate + and - signs for potential. Voltage between two points is the di ff erence between the potential of the two points (see figure). Voltage between two charge reservoirs is analogous to height di ff erence between two fluid reservoir and the same way, the potential of each point is analogous to its elevation compared to some reference ( e.g., sea level). + + 2 1 Potential v’ = v v’ = V V 2 1 1 v = V V 2 0 v v’ V V 2 1 2 Elevation 1 + - h h h h 0 h = - Sea Level MAE140 Notes, Winter 2001 1

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If we connect the charge reservoirs, electric charges flow from one to other. The rate of the charge flow through a specific area is called the electric current: i = dq dt Unit: Ampere (A = C/s) with the current flowing in the direction of the charge flow (it means that a positive current is associated with the flow of positive charge). In principle, electric charges generate an electric field and motion of the charged particles (current) generates a magnetic field. This electromagnetic field interacts with all charges and a ff ect them. The behavior of such a system is described by Maxwell’s equation. Solution of Maxwell’s equations, however, is di ffi cult and not needed expect for some cases (propagation of electromagnetic wave and light, antennas, etc.) In most relevant engineering cases the problem can be greatly simplified by noting that electric charges preferentially flow through a conductor (or a semiconductor) as opposed to vacuum, air, or any insulator. In this case, the system can be described as a circuit containing “circuit elements” and “connecting ideal wires.” Circuit theory is the scientific
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