INTRODUCTION TO CIRCUITS NOTES

WHAT IS A CIRCUIT?

• For electricity to flow from a battery to light up a light bulb, there must be a

complete path from the positive terminal on top of the battery to the negative

terminal on the bottom of the battery.

• The word circuit comes from the same root as the word circle – you can think

of it as a circular loop.

• A complete path is called a closed circuit. Electrons are “flowing”.

• If there is a gap or hole or opening in the path, it is called an open circuit

and the light bulb will not light up. Electrons are stationary.

BASIC ELECTRIC CIRCUIT

• Circuit when there is a continuous and conducting path between the positive and

negative terminals of a battery; through which charge can move or “flow”.

• Electrons are “pushed” away from the negative terminal of the battery and “pulled”

towards the positive terminal.

• The battery provides the force (we call it Voltage) which moves the charges (we call

this Current).

ELECTRIC CURRENT

• Current describes the amount of charge (number of electrons) flowing in

a circuit each second.

• Symbol: I

• Unit: Coulombs per second or Amperes or Amps

• 1 C/s=1 A

𝐼 =∆𝑄

∆𝑡𝐶𝑢𝑟𝑟𝑒𝑛𝑡 =

𝐶ℎ𝑎𝑟𝑔𝑒

𝑡𝑖𝑚𝑒

ACTUAL CURRENT VS. CONVENTIONAL CURRENT

•Actual current is electrons (-)

flowing from the – to the +

of a battery.

• Conventional current (the

one we will use) describes

the movement of + charges

from the + to the – of a

battery.

VOLTAGE

•Without a voltage source, current will not flow in a circuit.

•Another name for voltage is potential difference – it is when two sides

of a circuit have different amounts of potential (like + and -).

• Voltage – the change in electric potential energy per Coulomb of

charge.

• Symbol: V

• Unit: Joules per Coulomb or Volts

1 Volt = 1 Joule/Coulomb

VOLTAGE CONTINUED

• Increasing the voltage in a circuit

causes the current to increase.

• A battery doesn’t provide charge, it

provides energy to the charges

already there.

• A typical battery (AA, AAA, D)

provides 1.5 V

• In the U.S., household voltages are

usually between 110 V and 120 V

ELECTRICAL RESISTANCE

• In almost all circuits, the electrons flow with some opposition or

resistance.

• Resistance- opposition to flow of charge. You can think of

electrical resistance as similar to friction.

• Symbol: R

• Unit: Ohms (Ω – the Greek letter omega)

• Conductors such as metals have very low resistance in general.

RESISTANCE MATHEMATICALLY DEFINED

•Mathematically, resistance in a circuit is defined as the amount of

voltage needed to produce one amp of current (volts per amp)

• 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 =𝑉𝑜𝑙𝑡𝑎𝑔𝑒

𝐶𝑢𝑟𝑟𝑒𝑛𝑡𝑅 =

𝑉

𝐼

• Increasing resistance causes current to decrease

• Resistance is determined by wire length, thickness, and material

• Current in a circuit is determined by voltage and resistance:

• 𝐼 = 𝑉

𝑅

EXAMPLE 1: A SMALL HEATER HAS A RESISTANCE OF 200 Ω. WHEN THIS HEATER IS PLUGGED INTO A 120 V OUTLET, HOW MUCH CURRENT FLOWS THROUGH THE HEATER?

EXAMPLE 1 SOLUTION

R=200 Ohms

V=120 V

I=?

𝐼 =𝑉

𝑅=120𝑉

200Ω= 0.6 𝐴

EXAMPLE 2: LIGHT BULB B HAS 4 TIMES THE RESISTANCE OF LIGHT BULB A, HOW WILL THE CURRENTS THROUGH THE TWO BULBS COMPARE IF THEY ARE CONNECTED TO THE SAME BATTERY?

EXAMPLE 2 SOLUTION

VB=VA (same battery)

RB=4RA

𝑰𝑨 =𝑽𝑨

𝑹𝑨𝑰𝑩 =

𝑽𝑨

𝟒𝑹𝑨=

𝑰𝑨

𝟒

EXAMPLE 3: A FLASHLIGHT USING 2 1.5 V BATTERIES HAS 0.1 A OF CURRENT WHEN IT IS TURNED ON. HOW MUCH CURRENT WOULD FLOW IF YOU USED 3 BATTERIES INSTEAD OF 2?

EXAMPLE 3 SOLUTION

𝑰 =𝑽

𝑹

Using 3 batteries instead of 2 would increase voltage by a factor of 1.5.

𝑰 =𝟏. 𝟓𝑽

𝑹= 𝟏. 𝟓 ∗ 𝟎. 𝟏𝑨 = 𝟎. 𝟏𝟓 𝑨

ENERGY IN A CIRCUIT

•A battery gives energy to

electrons, as they move through

a device, they give their energy

up to another form (light, heat,

etc.)

ELECTRIC POWER

• Rate of energy transfer in a circuit

• Symbol: P

• Unit: Watts (W) = Joules/second

• Equation: 𝑷𝒐𝒘𝒆𝒓 = 𝑪𝒖𝒓𝒓𝒆𝒏𝒕 ∗ 𝑽𝒐𝒍𝒕𝒂𝒈𝒆 𝑷 = 𝑰𝑽

EXAMPLE 4: WHAT IS THE CURRENT IN A 60 WATT LIGHT BULB WHEN IT IS PLUGGED IN TO A 120 V OUTLET?

EXAMPLE 4 SOLUTION

P=60 W

V=120 V

I=?

𝑃 = 𝐼𝑉

𝐼 =𝑃

𝑉=60𝑊

120 𝑉= 0.5 𝐴

EXAMPLE 6: THE RESISTANCES OF SEVERAL DEVICES ARE GIVEN BELOW. WHICH WILL USE THE MOST POWER?HAIR DRYER - 12Ω LED – 1440Ω

EXAMPLE 6 SOLUTION

•Assume each device is plugged into the same outlet (voltage

doesn’t change).

• Increasing resistance decreases current 𝐼 =𝑉

𝑅

•P=IV, so if voltage stays the same, but current decreases – power

also decreases.

•The hair dryer uses the most power since it has the smallest

resistance.

CIRCUITS ANALOGY #1 – ROCKS ROLLING DOWN A HILL

• Imagine a rock laying on level ground. It will not move anywhere (no current)

since there is no difference in elevation (voltage).

However, an object at the top of a hill could

roll down (current flowing) because of the

elevation difference (voltage).

If there were bushes (resistance) on the hill,

fewer rocks would make it to the bottom

each second (current)

CIRCUITS ANALOGY #2 – WATER FLOWING THROUGH A PIPE OR HOSE

• The pump provides a

pressure difference (voltage)

and causes water to flow

(current) through the pipes.

• If there are a lot of kinks in

the hose (resistance), not as

much water gets through

(current).