Electric current and electric circuit

Every torch that glows, fan that spins, and phone that charges is running on the same simple idea: charge on the move. Electric current is nothing more than a measured rate — how much charge slips past a point in a wire every second — and an electric circuit is nothing more than a closed loop that lets that charge keep moving instead of piling up. This article builds both ideas from scratch: the definition and unit of current, the historical quirk of conventional current direction, the anatomy of a simple circuit (cell, wires, switch, device), and why an ammeter must sit in series to measure it honestly. These are the opening definitions of the CBSE Class 10 chapter "Electricity," and every later idea — Ohm's law, resistance, heating effects — is built directly on top of the formula $I = Q/t$ introduced here.

The core insight

Electric current is the rate of flow of charge, $I = Q/t$ , measured in amperes with an ammeter in series, and it flows (by convention) from a cell's positive terminal, around a closed circuit, back to its negative terminal.

The core idea

What current actually is. A conductor is full of charge carriers that, left alone, jostle about randomly with no net drift. Connect it into a closed loop with a cell, and an electric field pushes those carriers to drift steadily in one direction — that steady, directed flow of charge is electric current. If a charge $Q$ crosses a cross-section of the conductor in time $t$ , the current is defined as:

I = \dfrac{Q}{t}

where: $I$ is the current (ampere, A), $Q$ is the charge that flows (coulomb, C), and $t$ is the time taken (second, s). One ampere is defined directly from this ratio — a flow of exactly one coulomb of charge per second:

1\ \text{A} = \dfrac{1\ \text{C}}{1\ \text{s}}

The unit is named after André-Marie Ampère, and current is always measured with an ammeter connected in series, so the very same charge that flows through the device under test also flows through the meter — that is the only way the meter reads the true current, not a fraction of it.

Conventional current versus electron flow. Inside a metal wire, it is negatively charged electrons that actually drift — from the cell's negative terminal, through the wire, to its positive terminal. But the direction of current was fixed by convention long before electrons were even discovered: conventional current is defined as the direction positive charge would flow, which is exactly opposite to the real electron drift. So in the external circuit, conventional current runs from the positive terminal of the cell, through the wires and devices, to the negative terminal — even though electrons are physically moving the other way.

Anatomy of a circuit. An electric circuit is a continuous, closed path — a source (cell or battery), connecting wires, a switch (key), and one or more devices such as a bulb — arranged so current can loop all the way around. A closed circuit is one where this path is unbroken and current flows continuously; break the loop anywhere, say by opening the switch, and you get an open circuit, where no current flows at all. A single cell supplies a fixed potential difference; joining several cells positive-to-negative in a row makes a battery, giving a larger combined potential difference to push charge around the same kind of loop. The switch itself does nothing magical — it is simply a convenient, reusable way to make or break the same closed loop of wire on demand, without physically disconnecting and reconnecting wires every time.

Figure

A simple circuit loop with a cell switch bulb and an ammeter in series showing conventional current from positive to negative outside the cell

Derivation ACharge Delivered by a Steady Current over Any Time

Show, starting only from the definition $I = Q/t$ , that a current running steadily for several separate stretches of time delivers a total charge equal to the current multiplied by the total time added up — the algebraic fact that lets you treat "current on for 2 minutes, then 3 minutes" as one single calculation, which is exactly the kind of reasoning CBSE numericals quietly expect even though the chapter never spells it out as a separate rule.

Step 1. Start from the defining equation. For a steady (constant) current $I$ flowing for a time $t_1$ , the definition $I = Q_1/t_1$ rearranges to $Q_1 = I \times t_1$ — the charge delivered in that stretch.

Step 2. Extend to a second stretch. If the same steady current $I$ then continues for a further time $t_2$ , the same definition gives $Q_2 = I \times t_2$ for that stretch, because current being "steady" means the ratio $Q/t$ stays fixed at $I$ throughout.

Step 3. Add the two charges. The total charge delivered over both stretches is $Q_{\text{total}} = Q_1 + Q_2 = I t_1 + I t_2 = I(t_1 + t_2)$ . Since $t_1 + t_2$ is just the total elapsed time $t$ , this collapses back to $Q_{\text{total}} = I \times t$ — the same formula as for one continuous stretch.

Step 4. Read the result. As long as the current stays steady, it does not matter whether it flows in one unbroken stretch or several separate ones with the switch opened and closed in between — the total charge only depends on the current and the total time the switch was closed. This is why $I = Q/t$ is safely applied to a whole numerical problem even when a circuit is described as being switched on and off.

Worked example

A steady current flows through a wire and delivers a charge of 90 C in 1 minute. Find the current, and find how many electrons crossed the cross-section in that time (take the charge of one electron as $1.6 \times 10^{-19}\ \text{C}$ ).

Step 1. Write down what is given: $Q = 90\ \text{C}$ , $t = 1\ \text{minute} = 60\ \text{s}$ (always convert time to seconds before using $I = Q/t$ ).

Step 2. Apply the formula: $I = \dfrac{Q}{t} = \dfrac{90\ \text{C}}{60\ \text{s}} = 1.5\ \text{A}$ .

Step 3. For the electron count, divide the total charge by the charge on one electron: $n = \dfrac{Q}{e} = \dfrac{90}{1.6\times10^{-19}} = 5.6\times10^{20}$ electrons.

Answer: the current is 1.5 A, carried by roughly $5.6\times10^{20}$ electrons drifting through the wire in that one minute.

Competitive stretch

A current of 0.5 A flows through a bulb filament for 10 minutes, then the switch is opened for a while and closed again so the same 0.5 A flows for a further 5 minutes. Using the result from the derivation above, find the total charge that has flowed through the filament.

Step 1. Convert both times to seconds: $t_1 = 10\ \text{min} = 600\ \text{s}$ , $t_2 = 5\ \text{min} = 300\ \text{s}$ , so total time $t = 900\ \text{s}$ .

Step 2. Since the current is steady at 0.5 A throughout both stretches, apply $Q_{\text{total}} = I \times t = 0.5 \times 900 = 450\ \text{C}$ .

Answer: a total charge of 450 C flows through the filament, even though the switch was opened in between — only the current and the total closed-switch time matter.

Common traps

Mixing up the direction of conventional current with the direction of electron flow — conventional current goes from + to − outside the cell; electrons actually drift from − to +.
Forgetting to convert time into seconds before using $I = Q/t$ , especially when the problem states time in minutes or hours.
Treating a circuit with a switch as fundamentally different from one without — a switch is just a convenient way to open and close the same closed loop, not a separate kind of circuit.
Believing an ammeter can be connected in parallel like a voltmeter — an ammeter must always go in series, otherwise it can short-circuit the source and damage the meter.

Ask the tutor: Want to see how $I = Q/t$ connects to Ohm's law and resistance, the very next idea in this chapter?

Why do we still use conventional current when electrons are what actually move?

Conventional current was defined as the direction of positive charge flow long before J. J. Thomson discovered the electron in 1897. By the time scientists learned that electrons — not positive charges — carry current in metals, the convention was already built into every textbook, formula and instrument. Switching it now would mean rewriting every circuit diagram and formula sign convention, so physics simply kept the older definition: current flows from + to − outside the cell, opposite to actual electron drift.

If I open the switch halfway through a numerical problem, do I need two separate calculations?

Not if the current stays the same steady value whenever the switch is closed — the derivation above shows the charges from separate closed-switch stretches simply add up, so $Q = I \times t$ still works with $t$ as the total time the switch was closed. You only need separate calculations if the current itself changes between stretches (a different cell, a different bulb), because then each stretch has its own $I$ and you must add $Q_1 = I_1 t_1$ and $Q_2 = I_2 t_2$ separately.

Why must an ammeter be in series and not in parallel?

An ammeter is designed to have a very low resistance, precisely so it barely disturbs the circuit and lets the actual current pass straight through it — that only works if it is inserted directly into the loop, in series, so every electron passing through the component also passes through the meter. If you instead connect it in parallel (across a component), its low resistance offers a much easier path than the component, most of the current rushes through the meter instead of the component, and the meter can be damaged or the source effectively short-circuited.

Electric current and electric circuit

The core idea

Worked example

Competitive stretch

Common traps

Before this

Where this leads