Determine The Magnitude Of The Current In The (A) 8.0- And (B) 2.0-? Resistors In The Drawing.

Calculating resistance

Learn how to calculate resistance in series and parallel circuits, and how resistance depends on length of conductor.

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Resistors in series

Current

When resistors are connected in series, the current through each resistor is the same.

The current is the same at all points in a series circuit.

In the circuit below: I _S = I ₁ = I ₂ = I ₃

Cell connected in parallel to 3 resistors R1, R2 and R3. Cell has potential difference V S and current I S. R1 has pd V1 and current I1. R2 has pd V2 and current I2. R3 has pd V3 and current I3.

Voltage V (or potential difference)

When resistors are connected in series, the total of all the voltages (sometimes referred to as potential difference) across each component is equal to the voltage across the power supply.

In the circuit above:

V _S = V ₁ + V ₂ + V ₃

This is just a form of the law of conservation of energy .

The supply voltage is a measure of the energy supplied to each electron .

The voltage across each component is the electrical energy converted by each component.

Therefore, the energy supplied equals the energy converted – energy has not been created or destroyed in the circuit.

In a series circuit, the voltage across the power supply equals the sum of the voltages across each component.

Resistance

The total resistance R of two or more resistors connected in series is the sum of the individual resistances of the resistors.

For the circuit above the total resistance R is given by:

R = R ₁ + R ₂ + R ₃

Example

Find the total resistance of the circuit above.

Answer

This is a series circuit and so total resistance is found using the equation:

R = R ₁ + R ₂ + R ₃ + R ₄

R = \({4}\Omega + {8}\Omega + {2}\Omega + {12}\Omega\)

R = \({26}\Omega\)

The total resistance of the network of resistors is \({26}\Omega\) . This means that the four individual resistors can be replaced by one resistor of \({26}\Omega\) .

Adding resistors in series always increases the total resistance.

The current has to pass through each resistor in turn so adding an additional resistor adds to the resistance already encountered.

Resistors in parallel

Current

When resistors are connected in parallel, the current from the power supply is equal to the sum of the currents through each branch of the circuit.

In other words, the currents in the branches of a parallel circuit add up to the supply current.

In the circuit above:

I _S = I ₁ + I ₂ + I ₃

This relationship expresses the law of conservation of charge.

All electrons that set out from the supply must return to the supply and each electron can only pass through one parallel branch.

In a parallel circuit, the current from the power supply equals the sum of the currents in each branch of the circuit.

Voltage

In a parallel circuit, the voltage across each branch of the circuit equals the supply voltage.

For the circuit above:

V _S = V ₁ = V ₂ = V ₃

In a parallel circuit, the voltage across each branch equals the supply voltage.

Resistance

When resistors are connected in parallel, total resistance, R, is calculated using the equation:

\[\frac{1}{R}=\frac{1}{R}_{1}+\frac{1}{R}_{2}+\frac{1}{R}_{3}\]

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