# Lesson Explainer: Calculating the Electric Current in a Wire Science

In this explainer, we will learn how to calculate the electric current in a simple circuit.

A circuit is a path that electric charge can flow through.

Electric charge is measured in units of “coulombs.” The unit symbol for the coulomb is C; for example, the charge of an electron is expressed as C.

The flow of electric charge is electric current. Electric current is measured in units of “amperes.” The unit symbol for the ampere is A.

Coulombs and ampere are both commonly used when studying electricity, and it is important to remember that they measure different things. The coulomb measures charge, and the ampere measures the flow of charge.

One ampere of current is equal to one coulomb of charge passing a point in a wire in one second. We can measure how much charge passes over any length of time—it does not need to be only one second. We simply find current by dividing an amount of charge by how much time the charge was measured for.

Current can be calculated using the formula where represents the current, represents charge, and represents time.

### Definition: Electric Current in a Wire

The electric current, , in a wire can be found using the formula where represents an amount of charge that passes a point in the wire over some amount of time, .

We can practice using this equation by working through some examples.

### Example 1: Calculating Charge Flow given Current

The diagram shows an electric circuit containing a cell and a bulb. The current in the circuit is 2 amperes. How much charge flows past point in the circuit in 1 second?

Recall that one ampere of current is defined as one coulomb of charge passing by a point in one second.

We are told that the current in the circuit is 2 A.

Therefore, we know that 2 coulombs of charge passes point in 1 second.

### Example 2: Comparing Currents in Multiple Circuits

Fares sets up three circuits. He measures how much charge flows through each circuit in the same amount of time. His results are shown in the following table.

ChargeTime
Circuit 120 coulombs5 seconds
Circuit 225 coulombs5 seconds
Circuit 312 coulombs5 seconds

Which circuit has the greatest current?

Recall that current can be found using the formula where is the current, represents charge, and represents time.

We will substitute values from the table into the equation above to calculate current values , , and . The subscripts 1, 2, and 3 tell which circuit the current is measured for.

Substituting in the charge and time measurements form circuit 1, we have

Therefore, the current in circuit 1 is 4 amperes.

Moving on to circuit 2, we have

The current in circuit 2 is 5 amperes.

For circuit 3,

So the current in circuit 3 is 2.4 amperes.

Therefore, circuit 2 has the greatest current.

### Example 3: Comparing Currents in Multiple Circuits

The diagram shows two circuits, circuit 1 and circuit 2. In circuit 1, 28 coulombs of charge flows through the bulb in 14 seconds. In circuit 2, 9 coulombs of charge flows through the buzzer in 3 seconds. In which circuit is the current greater?

We want to compare the current in two different circuits. Recall the formula for calculating current, where is current, represents charge, and represents time. We can find the current in the circuits by substituting the given amounts of charge and time for each circuit into this equation.

For circuit 1, we have

So, we have found that the current in circuit 1 is 2 amperes.

For circuit 2, we have

The current in circuit 2 is 3 amperes.

Therefore, the current is greater in circuit 2.

### Example 4: The Relation between the Current and the Amount of Charge Moving in a Circuit

The diagram shows an electric circuit containing a cell and a bulb. The amount of charge flowing past point in one second is 12 coulombs. If the amount of charge flowing past point in one second were to double, by what factor would the current in the circuit change?

We want to understand how doubling the amount of charge flowing past a point affects the current in a circuit. We can start by remembering the formula for current, where is current, represents charge, and represents time. We will use this formula to find two current values, which we will call and . The subscripts and specify the circuit with the original or doubled amount of charge.

To calculate the original amount of current, we have so the current is originally 12 amperes.

After the amount of charge doubles, there is 24 coulombs passing point in one second. Substituting this into the equation, we have

After the charge is doubled, the current is 24 amperes.

Therefore, increasing the charge passing point in one second by a factor of 2 causes the current to increase by a factor of 2.

### Example 5: Understanding Electric Current in a Circuit

Describe what is meant by the phrase the electric current in a circuit.

We have been asked to write a short description of electric current in a circuit. To begin, recall that electric current is the movement of electric charge. Current measures how rapidly charge moves through something.

In a circuit, we see negatively charged electrons moving through a wire. We look at one point in the wire to measure its current.

Let us finish by summarizing some important concepts.

### Key Points

• Electric charge is measured in units of coulombs; the symbol for the coulomb is C.
• Electric current is measured in units of amperes; the symbol for the ampere is A.
• One ampere is equal to one coulomb passing a point in a wire in one second.
• We can calculate current, , using the formula , where represents an amount of charge passing a point in an amount of time, .