Electrical Circuit

Current

When we use electrical appliances, electric current flows in the circuit. The flowing current means that the electrons flow in thecircuit.

Current is defined as the rate of the flow of charge.

The unit of current is ampere [A].

The unit of charge is coulomb [C].

Formula for electric Current

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

I: Current [A]

Q: Charge [C]

t: time [s]

Instrument for measuring the current

- An ammeter must be connected to a componnent in series

- The positive terminal (usually red terminal) must be connected to the positive terminal of the battery.

- The negative terminal (usually black terminal) must be connected to the negative terminal of the battery.

Example

A motor uses a current of 20A for 10s. How much charge flows through it?

Solution

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

Given that

I = 20A

Q = ?

t = 10s

$\mathrm{20}=\frac{Q}{10}$

$Q=\mathrm{20}\times 10$

Answer: $Q=\mathrm{200C}$

Electromotive force

Electromotive force (e.m.f.) of a cell (or battery) is defined as the energy supplied to each coulomb of charge within it.

The unit of e.m.f. is volt [V]. (1V = 1J/C)

Formula for Electromotive force

$\mathrm{e.m.f}=\frac{E}{\mathrm{Q}}$

e.m.f.: Electromotive force [V]

E: Energy supplied by the cell [J]

Q: Charge flow through the cell [C]

Potential difference

Energy carried by charge form a cell or a battery is consumed in electrical components like resistor, lamp, bulb or heater of the circuit. For example, when the charges flow through the bulbs in a circuit, their energy is converted to light and heat energy. This consumed energy is called the potential difference across the component.

Potential difference (p.d.) is defined as the energy converted per unit charge passing through a component.

The unit of p.d. is volt [V].

$V=\frac{E}{\mathrm{Q}}$

V: Potential difference [V]

E: Energy converted to other forms in the component [J]

Q: Charge flow through the component [C]

Instrument for measuring p.d.

A voltmeter must be connected across a component in a circuit (parallel to a component).

The positive terminal (usually red terminal) must be connected to the positive terminal of the battery.

The negative terminal (usually black terminal) must be connected to the negative terminal of the battery.

Example 1

60 C of charge flow through a bulb which transfers 180J of energy into light. What is the potential difference?

Solution

$V=\frac{E}{\mathrm{Q}}$

Given that

Q = 60C

E = 180J

V = ?

$V=\frac{\mathrm{180}}{60}$

Answer:$V=\mathrm{3V}$

Example 2

When a current of 2.5A flows for 8s through a bulb, 240J of energy are consumed.

(a) How much charge flows through the bulb?

(b) What is the potential difference across the bulb?

Solutions

(a)

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

Given that

Q = ?

I = 2.5A

t = 8s

$\mathrm{2.5}=\frac{Q}{8}$

$Q=\mathrm{2.5}\times 8$

Answer: $Q=\mathrm{20C}$

(b)

Solution

$V=\frac{E}{\mathrm{Q}}$

Given that

Q = 20C

E = 240J

V = ?

$V=\frac{\mathrm{240}}{20}$

Answer: $V=\mathrm{12V}$