Nodal Voltage Calculator

Nodal Voltage Calculator (Single Node)






Result:

Calculated Nodal Voltage (V_node):

function calculateNodalVoltage() { var v1 = parseFloat(document.getElementById('voltageSource1').value); var r1 = parseFloat(document.getElementById('resistor1').value); var v2 = parseFloat(document.getElementById('voltageSource2').value); var r2 = parseFloat(document.getElementById('resistor2').value); var r3 = parseFloat(document.getElementById('resistor3').value); if (isNaN(v1) || isNaN(r1) || isNaN(v2) || isNaN(r2) || isNaN(r3)) { document.getElementById('calculatedVoltage').innerText = "Please enter valid numbers for all fields."; return; } if (r1 === 0 || r2 === 0 || r3 === 0) { document.getElementById('calculatedVoltage').innerText = "Resistor values cannot be zero."; return; } // Nodal analysis for a single node V_node connected to: // – V1 via R1 // – V2 via R2 // – Ground (0V) via R3 // KCL at V_node: (V_node – V1)/R1 + (V_node – V2)/R2 + (V_node – 0)/R3 = 0 // V_node * (1/R1 + 1/R2 + 1/R3) = V1/R1 + V2/R2 // V_node = (V1/R1 + V2/R2) / (1/R1 + 1/R2 + 1/R3) var numerator = (v1 / r1) + (v2 / r2); var denominator = (1 / r1) + (1 / r2) + (1 / r3); if (denominator === 0) { document.getElementById('calculatedVoltage').innerText = "Cannot calculate (denominator is zero). Check resistor values."; return; } var nodalVoltage = numerator / denominator; document.getElementById('calculatedVoltage').innerText = nodalVoltage.toFixed(4) + " Volts"; } .calculator-container { font-family: 'Arial', sans-serif; background-color: #f9f9f9; border: 1px solid #ddd; padding: 20px; border-radius: 8px; max-width: 600px; margin: 20px auto; box-shadow: 0 2px 4px rgba(0,0,0,0.1); } .calculator-container h2 { color: #333; text-align: center; margin-bottom: 20px; } .calculator-inputs label { display: block; margin-bottom: 5px; color: #555; font-weight: bold; } .calculator-inputs input[type="number"] { width: calc(100% – 22px); padding: 10px; margin-bottom: 15px; border: 1px solid #ccc; border-radius: 4px; box-sizing: border-box; } .calculator-inputs button { background-color: #007bff; color: white; padding: 12px 20px; border: none; border-radius: 4px; cursor: pointer; font-size: 16px; width: 100%; transition: background-color 0.3s ease; } .calculator-inputs button:hover { background-color: #0056b3; } .calculator-result { margin-top: 20px; padding: 15px; background-color: #e9ecef; border: 1px solid #dee2e6; border-radius: 4px; } .calculator-result h3 { color: #333; margin-top: 0; margin-bottom: 10px; } .calculator-result p { font-size: 1.1em; color: #007bff; font-weight: bold; }

Understanding Nodal Voltage Analysis

Nodal voltage analysis is a powerful circuit analysis technique used to determine the voltage at various nodes within an electrical circuit relative to a common reference node, typically ground (0 Volts). It simplifies complex circuits by focusing on node voltages rather than individual component currents, often leading to a system of linear equations that can be solved to find all unknown node voltages.

The Core Principle: Kirchhoff's Current Law (KCL)

The foundation of nodal analysis is Kirchhoff's Current Law (KCL), which states that the algebraic sum of currents entering a node (or leaving a node) in an electrical circuit is equal to zero. In simpler terms, charge cannot accumulate at a node; whatever current flows into a node must flow out of it.

When applying KCL, currents are typically expressed using Ohm's Law (I = V/R). For a current flowing from node A to node B through a resistor R, the current I is given by (V_A – V_B) / R.

How the Calculator Works (Single Node Example)

This specific calculator is designed to solve for the voltage at a single unknown node (let's call it V_node) in a simplified circuit configuration. Imagine a central node connected to three different paths:

  1. A path connecting V_node to a known Voltage Source V1 through a Resistor R1.
  2. A path connecting V_node to another known Voltage Source V2 through a Resistor R2.
  3. A path connecting V_node directly to Ground (0 Volts) through a Resistor R3.

By applying KCL at V_node, we sum the currents leaving the node and set them to zero:

  • Current leaving V_node towards V1: (V_node – V1) / R1
  • Current leaving V_node towards V2: (V_node – V2) / R2
  • Current leaving V_node towards Ground: (V_node – 0) / R3

So, the KCL equation becomes:

(V_node - V1)/R1 + (V_node - V2)/R2 + V_node/R3 = 0

Rearranging this equation to solve for V_node:

V_node * (1/R1 + 1/R2 + 1/R3) = V1/R1 + V2/R2

V_node = (V1/R1 + V2/R2) / (1/R1 + 1/R2 + 1/R3)

This calculator takes the values for V1, R1, V2, R2, and R3 as inputs and uses this formula to compute the unknown nodal voltage V_node.

Example Calculation

Let's use the default values provided in the calculator:

  • Voltage Source V1 = 10 Volts
  • Resistor R1 = 100 Ohms
  • Voltage Source V2 = 5 Volts
  • Resistor R2 = 50 Ohms
  • Resistor R3 = 200 Ohms (to Ground)

Using the formula:

V_node = (10/100 + 5/50) / (1/100 + 1/50 + 1/200)

V_node = (0.1 + 0.1) / (0.01 + 0.02 + 0.005)

V_node = 0.2 / 0.035

V_node ≈ 5.7143 Volts

This calculator provides a quick way to verify your manual calculations for this common nodal analysis problem.

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