PHYS1000 DC electric circuits 1

Electric circuits

Electric current

Charge can move freely in a conductor if an electric?eld is present;the moving charge is an electric

current (SI unit is the ampere (A),often shortened to amps).

We use the potential difference or voltage across the conductor to characterize the electric?eld

(since V = Ex)

The current that?ows is determined by the potential difference across the conductor and the

resistance of the conductor (Ohm’s law):

V = IR

The SI unit of resistance is the ohm(

).

As current?ows through a resistance,energy is lost:

P = VI

If the current is constant (which also means it doesn’t change direction),the current is called a direct

current or DC.

What is an electric circuit?

To maintain a steady electric current,the moving charge needs to be able to return to its starting

location?a complete circuit must be present.

Since energy lost as the charge moves,this energy must be replaced by a power supply.The main ways

to produce an electric current are generators using electromagnetic induction,and chemical batteries.

The exact type of power supply is not important,howmuch energy is supplied is.We measure this

energy by the potential difference provided by the power supply?also called the voltage of the

power supply.

Note that the potential difference across a resistance is a potential drop,or a reduction in energy.The

potential difference across a power supply is a potential rise?a gain in energy.

For a steady current,if we go around a complete circuit,the total energy supplied is equal to the total

energy lost:

∑

V

supply

=

∑

V

losses

Usually,a simple circuit will only contain a single power supply.If we make all potential rises

positive,and all potential drops negative,we can write:

∑

V = 0

around any closed circuit.

PHYS1000 DC electric circuits 2

Circuit diagrams

An easy way to describe an electric circuit is with a circuit diagram?a drawing showing the circuit.

Standard symbols are used for the various components in the circuit,and the conductors (wires)

joining themtogether are drawn as lines.

Circuit symbols:power supply

ADC power supply can be drawn in a number of different ways (we’ll use the one on the left):

9 V

+9 V

+−

ResistorsIf the resistance of a component of an electric circuit is its main electrical property,we can call it a

resistor.

Why do we want to add resistance to a circuit?

Acomponent might performsome useful function,but its main electrical property is resistance

?we can represent it with a resistor.(For example,a heating element,or a light bulb.)

We can use a resistor to control the current in a circuit.Once we put a resistor in a circuit,its

resistance is so much larger than the resistance of the wires in the circuit,and we can assume

that the resistance of the wires is zero.

Circuit symbols:resistor

Example:a 1.0 k

resistor connected to a 12 V power supply:

12 V

1.0 k

PHYS1000 DC electric circuits 3

Series ¶llel circuits

Multiple components in a circuit can either be connected

in series with each other

1

R

2

R

3

R

in parallel with each other

1

R

3

R

2

R

Series circuits

Example:a 1.0 k

and a 2.0 k

resistor connected in series with a 12 V power supply:

12 V

1.0 k2.0 k

Note that

as the current?ows fromAto B,power is lost in each resistor,so

V

AB

= V

1

+V

2

PHYS1000 DC electric circuits 4

the same current?ows through all the resistors

I

A

= I

1

= I

2

= I

B

the combined resistance of both resistors is

R

T

= R

1

+R

2

Example:a 1.0 k

and a 2.0 k

resistor connected in parallel with a 12 V power supply:

12 V

2.0 k1.0 k

Note that

all the resistors connect the same two points in the circuit together,so they must all have the

same potential difference across them

V

AB

= V

1

= V

2

the current at Asplits up to?owthrough all of the resistors

I

A

= I

1

+I

2

= I

B

the combined resistance of both resistors is

1

R

T

=

1

R

1

+

1

R

2

Measuring currents and voltages

We use ammeters and voltmeters to measure current and potential difference.

ammeterThe current to be measured must?owthrough the meter?connect in series

A

PHYS1000 DC electric circuits 5

voltmeterWe want to measure the potential difference across two points?connect in parallel across these two

points

V

BA

A multimeter is a convenient device that can measure either voltage or current (and resistance as

well).Capacitors

ADVANCED

Two parallel plates with positive and negative charges equal in magnitude can be used to store elec-

trical energy.This is called a capacitor.This energy can be used as a power supply in a circuit.The

stored energy depends on the charge and the capacitance (measured in farads (F)).

Q = CV

Since the potential difference between the two plates depends on the charge on the plates,the voltage

across the capacitor will fall as current?ows fromit?as the capacitor discharges.

Howquickly the voltage falls depends on howmuch current?ows,which depends on the resistance

in the circuit.

V = V

0

expt=RC

where R is the resistance in the circuit and C is the capacitance of the capacitor.The quantity RC is

called the time constant,and is usually written as .

Similarly,it takes time to charge a capacitor:

V = V

0

(1 expt=)

This can be used to measure time in DC circuits.

When the capacitor is fully charged or discharged,no current will?ow.

Circuit symbols:capacitor

PHYS1000 DC electric circuits 6

AC circuits

EXTRA

Another common type of electric current is alternating current,or AC.

In an AC circuit,the current varies sinusoidally,and?ows?rst in one direction,and then the other.

If a suitable average voltage and current are used for AC,Ohm’s Law can still be used for circuits

which only contain resistors.

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