Steady Current: MDCAT Physics notes

Electric current

Electric current is the rate of flow of charge through any cross-section of a conductor:

$$I = \frac{\Delta Q}{\Delta t}$$

• SI unit: ampere (A), a base unit. 1 A = 1 C s$^{-1}$.
• Unit of charge: coulomb. 1 C = 1 A s, the charge that passes a point when a current of 1 A flows for 1 s.
• Current is a scalar. It has a direction of flow along the wire, but currents meeting at a junction add algebraically, not by vector rules.

Example: 120 C passes a point in 40 s, so $I = 120/40 = 3$ A. Conversely a current of 0.5 A for 2 minutes carries $Q = 0.5\times120 = 60$ C.

Steady current

A steady current is one whose magnitude and direction do not change with time. To maintain a steady current a constant potential difference must be kept across the conductor, for example by a battery or cell.

A battery is a source of electrical energy with fixed polarity: its positive and negative terminals do not change, so it gives direct current. A generator of the AC type gives current that reverses periodically.

Charge carriers

Conventional current

Conventional current is taken as the flow of positive charge from the positive terminal to the negative terminal outside the source. Electrons in a metal actually drift in the opposite direction. A negative charge moving one way is equivalent to an equal positive charge moving the other way.

Effects of current

A flow of charge produces:

• a magnetic field around it (magnetic effect);
• heating in the conductor (heating effect, $I^2R$);
• chemical changes in electrolytes (chemical effect).

Moving charges carry their electric field with them and also produce a magnetic field.

Kirchhoff's first rule (junction rule)

The sum of currents entering a junction equals the sum of currents leaving it:

$$\sum I_{\text{in}} = \sum I_{\text{out}}$$

This rule is a statement of the law of conservation of charge: charge does not pile up or vanish at a junction. Kirchhoff's second rule (loop rule, $\sum\varepsilon = \sum IR$) is based on conservation of energy.

Example: 5 A and 3 A enter a junction and one wire leaves carrying 2 A. The other outgoing wire must carry $5 + 3 - 2 = 6$ A.

Key formulas

• $I = Q/t$
• 1 C = 1 A s
• Number of electrons $n = Q/e$, $e = 1.6\times10^{-19}$ C

Common MDCAT traps

• Current is a scalar even though it has a direction.
• The ampere is the unit of current; the coulomb is the unit of charge. In base units the coulomb is A s, not A m or J s$^{-1}$.
• Kirchhoff's first rule is conservation of charge, the second is conservation of energy.
• A steady current needs a constant, not a varying, potential difference.

Quick revision

• Current = rate of flow of charge.
• Steady current does not change with time.
• Battery has fixed polarity and gives DC.
• Flowing charge produces a magnetic field.
• 1 A = 1 C s$^{-1}$.