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Lock 4.

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Types of circuits.

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Series and parallel.

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Electricity.

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Series circuits.

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In these circuits, all the components are connected one after the other.

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This way, all the current flows through all the load devices.

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There is only one possible path for the electric current to flow through.

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The same current flows through all the load devices.

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If one load device stops working, none of them will work because the circuit will be open.

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This happens when one of the load devices fails or is not connected to the circuit properly.

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The energy supplied by the cell must be divided across all the load devices.

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In the circuit in the drawing on the left, the energy is divided among the three lamps,

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which all light up to the same level but do not shine as brightly as a single lamp would.

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Parallel circuits.

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In these circuits, the load devices are connected on different branches of the wire.

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There are several possible paths for the electric current to flow through.

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The electric current is split across all the possible paths

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and more current will circulate through the branch that offers the least resistance.

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The current intensity that flows through each load device is different.

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Even if one of the load devices stops working,

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the rest continue to work because the electric current takes another path,

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the circuit is closed by another path.

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The energy supplied by the cell reaches each branch of the circuit directly.

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Therefore, all the lamps shine with the same brightness as a single lamp located on a single branch.

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However, the cell will run down sooner.

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Series-parallel combination circuits.

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These circuits contain devices connected in series and in parallel.

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In this case, the circuits have properties of both series circuits and parallel circuits.

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Solving circuits.

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To learn how to solve circuits, we generally begin with circuits composed only of cells and resistors.

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The way that we put these resistors together is called the association of resistors.

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This gives us the three types of basic circuits that we have just seen.

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To calculate an unknown variable in a series, parallel or series-parallel combination circuit,

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we add all the resistors together and replace them with a single one, which we call the total resistance.

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This way, we make the circuit equivalent to a simple circuit with just one resistor.

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With this simple circuit, we can apply Ohm's law to make our calculations quickly

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and then calculate the values for each resistor.

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The circuit formed with the equivalent resistors is called an equivalent circuit.

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We can obtain two things from this circuit.

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The currents flowing through the circuit.

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The potential drops taking place across the components.

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Solving series circuits.

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To simplify things, we will solve a circuit formed by three resistors connected in series to a cell.

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We will solve it in the same way that we would solve any circuit with resistors connected in series,

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regardless of how many there are.

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We calculate the equivalent resistance of a series circuit

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by adding up the values of all the resistors in the circuit.

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In this case,

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Rt equals R1 plus R2 plus R3.

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And the equivalent circuit is one with only one resistor with the equivalent resistance.

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Since this circuit is equivalent to the last one,

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the current flowing through the two circuits will be the same.

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We apply Ohm's law to calculate the current flowing through the equivalent resistance.

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Since the resistors are in series,

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the current is the same in them all and it is equal to the total current of the circuit.

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By contrast, the total voltage or potential difference supplied by the cell or power source

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is divided across all the resistors.

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We can calculate this with Ohm's law.

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It must hold that all the energy supplied by the cell, Vt,

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will be equal to the potential drop across each resistor.

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Relationship between the variables of the real circuit and the equivalent circuit.

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The equivalent resistance is equal to the sum of all resistances in the circuit.

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The current flowing through all of the resistors in the circuit is the same

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and is equal to the current of the equivalent circuit.

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The total voltage delivered by the power source

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is the sum of the potential drops across each of the resistors.

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Worked example of a series circuit.

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From the series circuit shown in the figure,

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calculate the current flowing through each resistor and the potential drop across each one.

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First, we calculate the equivalent resistance by adding up all the resistances.

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The equivalent resistance is 500 Ohms.

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This figure shows the resulting equivalent circuit.

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We use Ohm's law to calculate the total current.

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This gives us 20 mA.

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Since this is a series circuit,

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the total current of the circuit is the same current that flows across each of the resistors in the circuit.

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To calculate the potential drops across each resistor,

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we apply Ohm's law in each resistor using the current values that we just calculated.

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We can check that we have done the exercise correctly by adding up the potential drops.

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The result should be equal to the total voltage supplied by the cell that is 10 volts.

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VT equals V1 plus V2 equals 4V plus 6V equals 10V.