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The branch of physics and technology concerned with the design of circuits using transistors and microchips, and with the behaviour and movement of electrons in a semiconductor, conductor, vacuum, or gas.

Mathematics concept explain through electronics project

A voltage divider is an essential concept in electronics that uses the ratio and proportion concept of mathematics. It is a simple circuit used to produce a voltage output that is a fraction of the input voltage. This circuit is commonly created using resistors in series.

Let's consider a simple voltage divider circuit with two resistors, R1 and R2, connected in series, supplied with an input voltage V_in. The output voltage V_out is taken across one of the resistors, which we'll designate as R2. The voltage divider uses the ratio of the two resistors to determine the output voltage.

The voltage across a resistor in a series circuit can be calculated using Ohm's Law: V = I * R, where V is the voltage across the resistor, I is the current flowing through the resistor, and R is the resistance of the resistor.

Since both resistors are in series, the current flowing through both R1 and R2 is the same. Let's call this current I_total.

Now, we can express the ratio of the output voltage to the input voltage as a proportion:

V_out / V_in = V_R2 / V_in = (I_total * R2) / V_in

Since I_total is the same for both resistors, we can simplify the equation:

V_out / V_in = R2 / (R1 + R2)

This is the voltage divider equation using the ratio and proportion concept. It tells us that the output voltage V_out is equal to the input voltage V_in multiplied by the ratio of R2 to the sum of R1 and R2.

In other words, the output voltage is determined by the fraction of R2's resistance over the total resistance in the circuit, which includes R1 and R2. This is why it is called a voltage divider—by varying the values of R1 and R2, you can adjust the output voltage to obtain a specific fraction of the input voltage.

Voltage dividers have numerous applications in electronics, such as setting reference voltages, biasing transistors, and scaling down signals for analog-to-digital converters, among others. Understanding the ratio and proportion concept in voltage dividers is crucial for designing and analyzing circuits where voltage scaling is required.