Series and Parallel Circuits, Summaries of Circuit Theory

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Series and Parallel

Circuits

How to Simplify to Find

Total Resistance, Current and

Voltage

Series Circuits

• Series Circuits are the simplest to work with.
• Here we have three resistors of different resistances. They share a single connection point. When added together the total resistance is 90-Ohms.

Calculating Total Resistance

of a Parallel Circuit

Two methods can be used to calculate the total resistance of the parallel circuit. They are the Product Over Sum equation or the Reciprocal Formula.

Product Over Sum is RT = (R1 x R2) (R1 + R2)

Reciprocal Formula is RT = 1 1 𝑅1+^

1 𝑅2+^

1 𝑅3+^

1 𝑅4+^

1 𝑅

Calculating Total Resistance of a Parallel Circuit

• So let use calculate RT in this circuit.
• RT = 1 1 𝑅1+^

1 𝑅2+^

1 𝑅3+^

1 𝑅4+^

1 𝑅

Series-Parallel Circuits

If we combined a series circuit with a parallel circuit we produce a Series-Parallel circuit.

• R1 and R2 are in parallel and

R3 is in series with R1 ǁ R2. The double lines between R and R2 is a symbol for parallel.

We need to calculate R1 ǁ R

first before adding R3.

Series-Parallel Circuits

• Here we can use the shorter Product Over Sum equation as we only have two parallel resistors.

R 1 ǁ 2 = (R1 x R2) (R1 + R2) =^

27 𝑥 34 27+34 =^

918 61 R 1 ǁ 2 = 15.049Ω + R3 = RT

RT = 15.049 + 58 = 73.049Ω

• RT = 73Ω

Series-Parallel Circuits

• Series-Parallel circuits can be more complex as in this case: In circuit (a) we have our original complex circuit. In circuit (b) we have resistors R 1 and R 2 combined to get 13.2Ω. R 4 is in series with the newly combined R 12 and their added value is 51.2Ω. And now (c) we are left with R 124 in parallel with R 3. (d) is our final circuit.

Series-Parallel Circuits

• Series, Parallel and Series-Parallel circuits are our three main types of circuits and they are common in DC and AC supplied circuits.
• A series circuit has one shared connection point between components.
• A parallel circuit has two shared connection points between components.

Series-Parallel Circuits

The End