Voltage Divider Virtual Laboratory

Electronics & Circuit Theory

PrayogSetu • Interactive Engineering & Virtual Instrumentation

SIMULATION ACTIVE
Electronics Lab
Quick Lab Presets:
Interactive Voltage Divider Schematic
IDEAL (UNLOADED) I = 0.800 mA
+ − 12.0 V I_total = 800.00 µA I_R2 R1 = 10.0 kΩ VR1 = 8.00 V P1 = 6.40 mW Vout R2 = 5.0 kΩ VR2 = 4.00 V P2 = 3.20 mW LOAD OFF RL = 10.0 kΩ V_RL = 0.00 V P_L = 0.00 mW 0V (GND) VOLTMETER (Vout) DC V 4.000 V Ratio: 33.33% of Vin
Attenuation Ratio (Vout/Vin): 0.3333 (33.33%)
Total Resistance (R_eq): 15.00 kΩ
Total Power Supplied: 9.60 mW
Loading Sag: 0.00% (No Load)
Live Formula & Step-by-Step Educational Derivation
REAL-TIME SOLVER
STEP 1

Parallel Load Equivalence

If a load RL is connected across R2, calculate their parallel equivalent R2,eff:

R2,eff = R2 = 5.00 kΩ (No Load)
Rtotal = R1 + R2 = 15.00 kΩ
STEP 2

Standard Voltage Divider Formula

Substitute values into the potential divider relation:

Vout = Vin × [ R2 / (R1 + R2) ]
Vout = 12.00 V × [ 5.00 kΩ / 15.00 kΩ ] = 12.00 V × 0.3333
Vout = 4.000 V
STEP 3

Current & Voltage Drops

Circuit loop current and individual resistor potential drops:

Itotal = Vin / Rtotal = 12.00 V / 15.00 kΩ = 0.800 mA
VR1 = Itotal × R1 = 8.000 V (66.7%)
VR2 = Vout = 4.000 V (33.3%)
STEP 4

Resistor Power Dissipations (P = V² / R)

Ensure thermal ratings are respected in practical circuits:

PR1 = (8.00 V)² / 10 kΩ = 6.400 mW
PR2 = (4.00 V)² / 5 kΩ = 3.200 mW
Ptotal = Vin × Itotal = 9.600 mW
Live Transfer Characteristics Graph
Vout vs R2 Sweep (Unloaded)
Ideal Response (No Load)
Loaded Response (RL Active)
Operating Q-Point
ACADEMIC & INDUSTRIAL REFERENCE MANUAL

Voltage Divider Circuit Theory & Engineering Principles

A rigorous guide to potential attenuation, series loop analysis, loading impedance matching, and practical circuit design rules.

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1. Fundamental Working Principle & KVL Derivation

A Voltage Divider (or potential divider) is a fundamental linear passive circuit that produces an output voltage (Vout) that is a calibrated fraction of its input voltage (Vin).

According to Kirchhoff's Voltage Law (KVL) and Ohm's Law for a series circuit with two resistors:

I = Vin / (R1 + R2) Vout = VR2 = I × R2 = Vin × [ R2 / (R1 + R2) ]

The dimensionless ratio α = R2 / (R1 + R2) is the voltage division factor, bounded strictly between 0 ≤ α ≤ 1. The voltage across R1 is complementarily VR1 = Vin × [ R1 / (R1 + R2) ].

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2. Loading Effect, Sag & Thévenin Equivalent

When an external load with resistance RL is connected across Vout, it forms a parallel combination with shunt resistor R2, reducing the lower branch impedance:

R2,eff = R2 || RL = (R2 × RL) / (R2 + RL) Vout,loaded = Vin × [ R2,eff / (R1 + R2,eff) ] < Vout,ideal

Thévenin Equivalent Model: Viewed from the output terminals, the divider behaves as an ideal voltage source Vth = Vout,ideal in series with an internal output resistance Rth = R1 || R2.

Engineering Design Rule (The 10× / 100× Rule): To prevent severe voltage sag, the load resistance should be at least 10 to 100 times larger than the divider output impedance (RL ≥ 10 × R2 for <9% error; RL ≥ 100 × R2 for <1% error).

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3. Potentiometer as a Variable Divider

A potentiometer is a three-terminal resistive component with a continuous resistive track of total resistance Rpot and an adjustable center wiper terminal:

  • The wiper physically divides the total track into two complementary series resistances: R1 = (1 - k) × Rpot and R2 = k × Rpot, where k ∈ [0, 1] is the fractional wiper position.
  • The output voltage is strictly linear with wiper displacement: Vout = k × Vin.
  • Widely utilized for manual setpoint calibration, analog volume controls, and angular/linear position displacement sensing.
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4. Industrial Applications & Best Practices

  • Microcontroller & ADC Input Level Scaling: Attenuating high industrial signal levels (such as 0–10V, 0–24V, or 12V automotive bus lines) down to safe microcontroller ADC ranges (0–3.3V or 0–5V).
  • Sensor Transduction Networks: Pairing a fixed reference resistor with variable sensors (like LDR photoresistors, NTC/PTC thermistors, and flex sensors) to translate physical resistance changes into readable analog voltage fluctuations.
  • Transistor Amplifier DC Biasing: Supplying a thermally stable Q-point DC base voltage in Common-Emitter BJT and Common-Source FET amplifier topologies.
  • Op-Amp Reference Thresholds: Supplying precision bias references to analog comparators, Schmitt triggers, and differential instrumentation stages.