When we look at how circuits work with series and parallel setups, it can really change how things function.
In a series circuit, the total resistance is simply the total of all the resistors added together:
[ R_{total} = R_1 + R_2 + ... + R_n ]
The same electric current flows through every part of the circuit. This means that the current remains the same everywhere. Because of this, the amount of voltage dropped across each resistor can be found like this:
[ V_i = I \cdot R_i ]
So, the total voltage drop would be:
[ V_{total} = V_1 + V_2 + ... + V_n ]
When we add more parts to a series circuit, the total resistance goes up, which makes the overall current go down:
[ I = \frac{V_{source}}{R_{total}} ]
In a parallel circuit, we find the total resistance a bit differently:
[ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n} ]
Here, all parts of the circuit share the same voltage from the source. However, each resistor can have a different current, calculated like this:
[ I_i = \frac{V_{source}}{R_i} ]
This way, the total current in a parallel circuit is higher, since it adds up all the current from each branch:
[ I_{total} = I_1 + I_2 + ... + I_n ]
Two important rules, known as Kirchhoff's Laws, help us understand circuits better:
Voltage Law: In any closed loop of a circuit, if you add up all the voltage changes, the total must equal zero.
Current Law: The total current that comes into a junction must be the same as the total current leaving that junction. This shows how current spreads out in parallel circuits.
In summary, series circuits split the voltage and have higher resistance, while parallel circuits spread out the current and have lower overall resistance. Knowing how these configurations work helps us design circuits that are better and more efficient.
When we look at how circuits work with series and parallel setups, it can really change how things function.
In a series circuit, the total resistance is simply the total of all the resistors added together:
[ R_{total} = R_1 + R_2 + ... + R_n ]
The same electric current flows through every part of the circuit. This means that the current remains the same everywhere. Because of this, the amount of voltage dropped across each resistor can be found like this:
[ V_i = I \cdot R_i ]
So, the total voltage drop would be:
[ V_{total} = V_1 + V_2 + ... + V_n ]
When we add more parts to a series circuit, the total resistance goes up, which makes the overall current go down:
[ I = \frac{V_{source}}{R_{total}} ]
In a parallel circuit, we find the total resistance a bit differently:
[ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n} ]
Here, all parts of the circuit share the same voltage from the source. However, each resistor can have a different current, calculated like this:
[ I_i = \frac{V_{source}}{R_i} ]
This way, the total current in a parallel circuit is higher, since it adds up all the current from each branch:
[ I_{total} = I_1 + I_2 + ... + I_n ]
Two important rules, known as Kirchhoff's Laws, help us understand circuits better:
Voltage Law: In any closed loop of a circuit, if you add up all the voltage changes, the total must equal zero.
Current Law: The total current that comes into a junction must be the same as the total current leaving that junction. This shows how current spreads out in parallel circuits.
In summary, series circuits split the voltage and have higher resistance, while parallel circuits spread out the current and have lower overall resistance. Knowing how these configurations work helps us design circuits that are better and more efficient.