Voltage Dividers and Current Dividers

1. Voltage Divider

A voltage divider is a simple circuit that uses resistors to split the input voltage into smaller voltages.

How it works: Imagine you have a battery or power source, and you want to get a smaller voltage for a specific part of the circuit. A voltage divider allows you to reduce the voltage by using two resistors connected in series (one after the other). The voltage gets split across the resistors depending on their values.

Formula: The voltage across each resistor in a series circuit is proportional to its resistance.

V_out = V_in * (R2 / (R1 + R2))

Where:

V_out is the output voltage across resistor R2.
V_in is the total input voltage.
R1 and R2 are the resistors in series.

Example: If you have a 12V battery and two resistors:

R1 = 4Ω
R2 = 6Ω

The total resistance is R1 + R2 = 4Ω + 6Ω = 10Ω.
Now, using the formula:

$V_{text{out}} = 12V times frac{6Ω}{(4Ω + 6Ω)} = 12V times frac{6}{10} = 7.2V$

So, you’ll get 7.2V across R2.

2. Current Divider

A current divider is the opposite of a voltage divider. It divides the total current into smaller parts across resistors that are connected in parallel.

How it works: If you have resistors in parallel, the current from the power source splits between them. The current that flows through each resistor is inversely proportional to its resistance. This means that the lower the resistance, the more current flows through it.

Formula: The current divider formula can be written as:

I1 = I_total * (R_total / R1)
I2 = I_total * (R_total / R2)

Where:

I_total is the total current.
R_total is the total resistance of the parallel resistors.
R1, R2 are the individual resistances.
I1, I2 are the currents through each resistor.

Example: Suppose you have a current of 10A and two resistors in parallel:

R1 = 2Ω
R2 = 6Ω

First, calculate the total resistance (R_total) for parallel resistors:

1/R_total = (1/R1) + (1/R2)
1/R_total = (1/2) + (1/6) = (3 + 1) / 6 = 4/6
R_total = 6/4 = 1.5Ω

Now use the current divider formula for each resistor:

I1 = 10A * (1.5Ω / 2Ω) = 7.5A
I2 = 10A * (1.5Ω / 6Ω) = 2.5A

So, the current through R1 is 7.5A and through R2 is 2.5A.

Summary

Voltage Divider: Splits voltage across resistors in series. The voltage depends on the ratio of resistances.
Current Divider: Splits current across resistors in parallel. The current depends on the ratio of the total resistance to each individual resistance.

Both of these concepts are based on Ohm’s Law and are used to control how voltage or current is distributed across a circuit!

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