CHAPTER 1 - Fundamentals of Electrical Circuits
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(1.2-1)
∫
Figure 1.2-2 between a and b can be calculated
along any a-b path if the field is conservative.
Equation (1.2-1) demonstrates how, under certain assumptions, electric circuit analysis may
be greatly simplified by using a scalar quantity, voltage, in place of the electric field, which is vector
entity and hence more complex to handle. In particular in DC and AC circuits the interest is in what
happens at the terminals of each component, for example the voltage at the terminals of a resistor
or capacitor or the voltage drop across it. Since a uniform and conservative field exists in resistors,
capacitors and inductors
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, voltage may be used to characterise the effect of the electric field on such
components.
This simplification, which uses a scalar quantity (voltage) to represent the effects of an electric
field (vector) and is appropriate for AC and DC circuits, may not apply when higher frequencies are
used as we will see in due course. What should also be pointed out is that voltage is not a physical
quantity, it simply represents an effect of the real entity which causes it i.e. the electric field. The
presence of water in the reservoir is an effect of the pump pushing the water up to it, so the pump is
what physically changes the level of water in the reservoir, the reservoir filling up is just an effect
which may be quantified and used to represent the work done by the pump.
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This is true only for ideal components however it is a good enough approximation in most practical cases
when only passive circuit elements are involved and the frequency of excitation remains low.
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