SIMPLE CIRCUITS

DC CIRCUITS DC cicuits include a power supply, one or more load devices that convert electrical energy into another type of energy, and conductors that make a closed loop. All three of these must be present for a circuit to work properly. It is called DC because the current only runs in one direction: from the positive terminal of the power supply to the negative terminal

VOLTAGE Voltage is the difference in electric potential between two places A battery provides charges with high electric potential and takes them back in at the other terminal with low electric potential. The difference is the voltage of the battery Symbol: V Units: Volts Unit symbol: V

CURRENT Current is the number of charges moving per second A power supply usually has a fixed voltage, but the current that runs in the circuit can vary depending on what’s connected to it I = Q/t Symbol: I Units: amps Unit symbol: A

RESISTANCE Resistance is what the load devices provide to the circuit. Their job is to convert the electrical energy of the charges to another form of energy, depending on what type of load device they are Resistance can be controlled by how you arrange the loads in the circuit. Symbol: R Unit: ohms Unit symbol: Ω

OHM’S LAW Ohm’s law tells us the relationship between voltage and current in a circuit. V = IR Resistors that obey Ohm’s law by having constant resistance are called ohmic resistors. There are others that have resistance that varies over time (for example, by getting hotter, which increases their resistance), which are called non-ohmic resistors

SERIES CIRCUITS In a series circuit, the load devices are arranged in a line: Because there is only one branch, the current is the same everywhere in the circuit. However, the voltage will be shared over all three load devices, depending on how much resistance each one has

RESISTORS IN SERIES We add resistors in series simply: R TOT = R 1 + R 2 This means that the total resistance in any series circuit or part of a circuit will be bigger than any of the resistors that make it up This means that series circuits tend to draw smaller currents Any one component breaking in a series circuit will break the rest of the circuit because there is only one branch for the current

PARALLEL CIRCUITS In a parallel circuit, the devices are arranged on different branches of the circuit. Because there is more than one branch, the current is shared between them, depending on the resistance in each branch. However, because each branch has the same relationship with the power supply, the voltage is the same across the branches

RESISTORS IN PARALLEL

COMBINED CIRCUITS Some circuits contain both parallel and series components. You can resolve these to find the total resistance by following some simple rules: 1.Combine any series components that are themselves part of a parallel branch 2.Combine parallel branches 3.Combine the parallel total with any remaining series components Although this may look difficult, it is easy to see with an example

EXAMPLE COMBINED CIRCUIT In the diagram below, there are both series and parallel sections: The 4Ω resistor and the 12Ω resistor are in series with each other. After combining them, we can then combine the total with the 20Ω resistor, in parallel. Finally, we can combine all that with the 6Ω resistor, in series with the total. 6Ω6Ω 22 Ω 8Ω 20 Ω

WORKING 1.Combine first series section: R 1 = = 30Ω 2.Combine this with the 20Ω resistor, in parallel 1/R 2 = 1/30 + 1/20 1/R 2 = 1/12 R 2 = 12Ω 3.Combine the parallel total with the last resistor R tot = R tot = 18Ω

CURRENT AND VOLTAGE LAWS Now you can use the combined resistance to find voltages and currents around the circuit using current and voltage laws Voltages around a loop add up to zero – the amount provided by the power supply is used up by the resistors Currents into and out of junctions add up to zero – the amount flowing through the main branch is shared between parallel branches This might look difficult, but is easy to see using an example

CURRENT AND VOLTAGE EXAMPLE We can find the unknown voltages and currents in the circuit below by following the rules 1.Find the total current in the circuit V = 9V R tot = 18Ω I = V/R = 9/18 = 0.5A 6Ω6Ω 22 Ω 8Ω 20 Ω 9V

CURRENT AND VOLTAGE EXAMPLE 2. Find the voltage across the 6Ω resistor R = 6ΩV = IR I = 0.5A = 0.5 x 6 = 3V 3. Find the voltage across the 20Ω resistor V = 9 – 3 = 6V

CURRENT AND VOLTAGE EXAMPLE 4. Find the current through the 20Ω resistor V = 6VI = V/R R = 20Ω = 0.3A 5. Find the current through the 22Ω and 8Ω resistors I = 0.5 – 0.3 = 0.2A

CURRENT AND VOLTAGE EXAMPLE 6. Find the voltage across the 8Ω resistor I = 0.2AV = IR R = 8Ω = 0.2 x 8 = 1.6V 7. Find the voltage across the 22Ω resistor V = 6 – 1.6 = 4.4V