Series Circuits: Difference between revisions
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:::<math>V=IR</math>; it can be rearranged to yield <math>I=\frac{V}{R}</math> and <math>R = \frac{V}{I}</math> | :::<math>V=IR</math>; it can be rearranged to yield <math>I=\frac{V}{R}</math> and <math>R = \frac{V}{I}</math> | ||
<br /> | <br /> | ||
:Total Resistance in a series circuit is the sum of all resistances. It can be used to find the overall current in the circuit, which can then be used to find individual resistances. | |||
::Total resistance is described by: | |||
:::<math>R_T=\sum_{n=1}^N {R}_{Series}=R_1+R_2+R_3+...R_N</math> | |||
Revision as of 16:04, 30 November 2015
claimed by Mchan46
Main Idea
- A Series Circuit is a simple type of electrical circuit in which components are placed in succession of one another.
- The electrical connection is not branched in any way. One can visualize this circuit as simply a closed loop.
- Often times, the simple series circuit may include but are not limited to: a number of resistors, switches, and of course, batteries.
- Keep in mind, if there is an open switch or break in the circuit no current flows.
A Mathematical Model
- Kirchhoff's Current and Voltage Laws apply in a series circuit.
- Through Kirchhoff's Current Law, we know that the sum of all current going in must equal the sum of all current going out.
- [math]\displaystyle{ \sum{I}_{in} - \sum{I}_{out} = 0 }[/math]
- Since there are no nodes for the current to split up, the current throughout a series circuit will always be the same through each component.
- Through Kirchhoff's Voltage Law, the sum of all voltage in a closed system must be zero.
- [math]\displaystyle{ \sum{V}_{Battery} - \sum{V}_{Components} = 0 }[/math]
- Through Kirchhoff's Current Law, we know that the sum of all current going in must equal the sum of all current going out.
- Ohm's Law is extremely useful in finding the voltages, resistances, and current throughout the series circuit.
- Ohm's Law gives us the following formula:
- [math]\displaystyle{ V=IR }[/math]; it can be rearranged to yield [math]\displaystyle{ I=\frac{V}{R} }[/math] and [math]\displaystyle{ R = \frac{V}{I} }[/math]
- Ohm's Law gives us the following formula:
- Total Resistance in a series circuit is the sum of all resistances. It can be used to find the overall current in the circuit, which can then be used to find individual resistances.
- Total resistance is described by:
- [math]\displaystyle{ R_T=\sum_{n=1}^N {R}_{Series}=R_1+R_2+R_3+...R_N }[/math]
- Total resistance is described by:
A Computational Model
- The best way to visualize a series circuit is to draw a schematic, which is a simplified representation of the circuit in real life.
- Resistors are usually represented in a schematic with
- Batteries are represented in a schematic by
- Switches can be open or closed. An open switch is represented by
Examples
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