Electric Current Explained: Definition, Formula, Types, and Uses

 Current

The idea of “transfer of charge” or “charge in motion” is of vital importance to us in studying electric circuits because, in moving a charge from place to place, we may also transfer energy from one point to another. The familiar cross-country power transmission line is a practical example of a device that transfers energy. Of equal importance is the possibility of varying the rate at which the charge is transferred to communicate or transfer information. This process is the basis of modern communication systems, including satellite global positioning systems, 5G (and beyond), and WiFi Internet connections.

The current flowing in a discrete path, such as a metallic wire, has both a numerical value and a direction associated with it; it is a measure of the rate at which charge is moving past a given reference point in a specified direction. Once we have specified a reference direction, we may then let q(t) be the total charge that has passed the reference point since an arbitrary time t = 0, moving in the defined direction. A contribution to this total charge will be negative if a negative charge is moving in the reference direction, or if a positive charge is moving in the opposite direction. As an example, Fig. 2.2 shows a history of the total charge q(t) that has passed a given reference point in a wire (such as the one shown in Fig. 2.1). We define the current at a specific point and flowing in a specified direction as the instantaneous rate at which net positive charge is moving past that point in the specified direction. This, unfortunately, is the historical definition, which came into popular use before it was appreciated that current in wires is actually due to negative, not positive, charge motion. Current is symbolized by I or i, and so

i = dq/dt...................... ​​ [1]

The unit of current is the ampere (A), named after A. M. Ampère, a French physicist. It is commonly abbreviated as an “amp,” although this is unofficial and somewhat informal. One ampere equals 1 coulomb per second.Using Eq. [1], we compute the instantaneous current corresponding to Fig. 2.2 and obtain Fig. 2.3. The use of the lowercase letter i is again to be associated with an instantaneous value; an uppercase I would denote a constant (i.e., time-invariant) quantity. The charge transferred between time t0 and t may be expressed as a definite integral:

∫q(t0)q(t)​​dq = ∫t0tidt′ ................................[2]

The total charge transferred over all time is thus given by

​q(t) = ∫t0ti dt′ + q(t0)

Several different types of current are illustrated in Fig. 2.4. A current that is constant in time is termed a direct current, or simply dc, and is shown in Fig. 2.4a. We will find many practical examples of currents that vary sinusoidally with time (Fig. 2.4b); currents of this form are present in normal household circuits. Such a current is often referred to as alternating current, or ac. Exponential currents and damped sinusoidal currents (Fig. 2.4c and d) will also be encountered later. We create a graphical symbol for current by placing an arrow next to the conductor. Thus, in Fig. 2.5a, the direction of the arrow and the value 3 A indicate either that a net positive charge of 3 C/s is moving to the right or that a net negative charge of −3 C/s is moving to the left each second. In Fig. 2.5 b, there are again two possibilities: either −3 A is flowing to the left or +3 A is flowing to the right. All four statements and both figures represent currents that are equivalent in their electrical effects,

and we say that they are equal. A non-electrical analogy that may be easier to visualize is to think in terms of a personal savings account: e.g., a deposit can be viewed as either a negative cash flow out of your accountor a positive flow into your account. It is convenient to think of current as the motion of positive charge, even though it is known that current flow in metallic conductors results from electron motion. In ionized gases, in electrolytic solutions, and in some semiconductor materials, however, positive charges in motion constitute part or all of the current. Thus, any definition of current can agreewith the physical nature of conduction only part of the time. The definition and symbolism we have adopted are standard. We must realize that the current arrow does not indicate the “actual” direction of current flow but is simply part of a convention that allows us to talk about “the current in the wire” in an unambiguous manner. The arrow is a fundamental part of the definition of a current! Thus, to talk about the value of a current i1(t) without specifying the arrow is to discuss an undefined entity. For example, Fig. 2.6a and b are meaningless representations of i1(t), whereas Fig. 2.6c is complete.