Calculating Circuit Resistance (Mod.2 sect.2 part1) 1 of 2

Series Circuit Schematic Example

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Caption: : A typical series circuit has its components connected end-to-end. All of the circuit current flows through each of the circuit components.

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Parallel Circuit Schematic Example

Caption: : The current in this parallel circuit (I) flows from the battery and then separates onto three circuit paths (I1 , I2 and I3).

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To calculate the total resistance in this series circuit, simply add the values of the two resistors: 300 ohms + 500 ohms=800 ohms

Caption: : *wow*

Calculating Resistance in a Series Circuit

Calculating Resistance in Parallel Circuits

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If a parallel circuit contains resistors of equal value, the total circuit resistance will be equal to a fraction of the value of one resistor. So, if a parallel circuit contains two equal resistors, then the total circuit resistance is equal to one-half the value of either resistor. If the circuit contains three equal resistors, the total circuit resistance is equal to one-third of the value of one resistor. If the circuit contains four equal resistors, the total circuit resistance is equal to one-fourth the value of one resistor, and so on. This figure shows a circuit containing two 1,000 Ω resistors connected in parallel. The total resistance in this circuit is equal to one-half of 1,000 (that is, 1,000 ÷ 2). Therefore, the total circuit resistance is 500 Ω.

Caption: : Since both parallel resistors are of the same value, the total resistance is equal to one-half the value of either resistor.

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Calculating Resistance in Parallel Circuits

If two resistors with different values are connected in parallel, you’ll need to use a different method to calculate the total circuit resistance. To find the total resistance in such a circuit, use the formula shown in this figure.

Caption: : This parallel circuit contains two resistors with different values. You must use the formula shown to calculate the total resistance.

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Calculating Resistance in Parallel Circuits

As shown, the values of the three resistors are 100 Ω, 200 Ω, and 300 Ω. To calculate the total resistance, first use the formula to calculate the total resistance of R1 and R2. Then, use that value and the value of R3 to calculate the total circuit resistance. The answer is 54.55 ohms.

Caption: : This circuit contains these resistors connected in parallel.

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Calculating Resistance in Parallel Circuits

Another method you can use to find the total resistance of a parallel circuit is the reciprocal method. Every number has a reciprocal. The reciprocal of a given number is one divided by the number. So, the reciprocal of 5 is 1/5. The reciprocal of 12 is 1/12.  To find the total resistance of a parallel circuit using the reciprocal method, first find the reciprocal of each resistor value (1/20, 1/40, 1/50). Then, add all the reciprocal values together after simplifying the fractions to decimals (0.095). Finally, find the reciprocal of that value to get the total resistance. The answer for this figure is 10.53 ohms.

Caption: : This circuit contains three resistors connected in parallel.

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Resistance in Series-Parallel Circuits

Caption: : This circuit contains four resistors connected in both series and parallel arrangements.

The first step is to find the resistance of the parallel portion of the circuit. This value can easily be found by using the resistance formula (13.33 ohms). Next, substitute this value for the parallel section in the circuit diagram. With this substitution, the circuit diagram is now a simple series circuit.  Finally, simply add the remaining resistor values together to get the total resistance for this circuit. The answer is 53.33 ohms.