Resistive Voltage Divider

Yaser Rahmati | یاسر رحمتی

Definition

The simplest, easiest to understand, and most basic form of a passive voltage divider network is that of two resistors connected together in series. This basic combination allows us to use the Voltage Divider Rule to calculate the voltage drops across each series resistor.

Voltage Divider Circuit

Here the circuit consists of two resistors connected together in series: $R_{1}$, and $R_{2}$. Since the two resistors are connected in series, it therefore follow that the same value of electric current must flow through each resistive element of the circuit as it has nowhere else to go. Thus providing an $I\times R$ voltage drop across each resistive element.

With a supply or source voltage, $V_{S}$ applied across this series combination, we can apply Kirchhoff’s Voltage Law, (KVL) and also using Ohm’s Law to find the voltage dropped across each resistor derived in terms of the common current, I flowing through them. So solving for the current ($I$) flowing through the series network gives us:

$$V_{s}=V_{R1}+V_{R2}=I\times R_{1}+I\times R_{2}\Rightarrow I=\frac{V_{s}}{R_{1}+R_{2}}$$

Hence, we can calculate the voltage dropped across resistor, $R_{2}$ in the above series circuit as being:

$$V_{O}=\frac{R_{2}}{R_{1}+R_{2}}V_{s}$$

Example

Voltage Divider Circuit Diagram

Python

def calculate_voltage_divider(R1, R2, V):
    total_resistance = R1 + R2
    voltage_across_R2 = V * (R2 / total_resistance)
    voltage_across_R1 = V - voltage_across_R2
    return voltage_across_R1, voltage_across_R2

R1 = float(input("Enter the value of resistor R1: "))
R2 = float(input("Enter the value of resistor R2: "))
V = float(input("Enter the value of the DC voltage source V: "))

voltage_R1, voltage_R2 = calculate_voltage_divider(R1, R2, V)

print("Voltage across R1: ", voltage_R1)
print("Voltage across R2: ", voltage_R2)

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