Please enter valid positive numbers. Current cannot be zero.
Thevenin Resistance ($R_{th}$): 0 Ω
Equivalent Conductance ($G_{th}$): 0 S
Max Power Transfer ($P_{max}$): 0 W
What is Thevenin Resistance?
In electrical engineering, Thevenin's Theorem states that any linear electrical network with voltage and current sources and only resistances can be replaced at terminals A-B by an equivalent voltage source $V_{th}$ in series connection with an equivalent resistance $R_{th}$.
The Thevenin Resistance ($R_{th}$) represents the internal resistance of the network as seen from the load terminals. Calculating this value is essential for impedance matching and understanding how a circuit will behave when connected to various loads.
How to Calculate Thevenin Resistance
There are two primary methods to find $R_{th}$:
The Source Deactivation Method: Turn off all independent sources (replace voltage sources with short circuits and current sources with open circuits). Calculate the total resistance between terminals A and B.
The $V_{oc}/I_{sc}$ Method: This is the method used by our calculator above.
Step 1: Measure the open-circuit voltage ($V_{oc}$) at the terminals.
Step 2: Measure the short-circuit current ($I_{sc}$) by placing a wire across the terminals.
Imagine a circuit where the measured open-circuit voltage is 24V. When you short the output terminals with an ammeter, you measure a current of 2 Amperes.
Formula: $R_{th} = V_{oc} \div I_{sc}$ Calculation: $24V \div 2A = 12 \Omega$ Result: The Thevenin Resistance is 12 Ohms.
The Importance of $R_{th}$ in Power Transfer
Thevenin resistance is critical for the Maximum Power Transfer Theorem. To extract the maximum amount of power from a network, the external load resistance ($R_L$) must be equal to the Thevenin resistance ($R_{th}$). Our calculator automatically computes $P_{max}$ using the formula: $P_{max} = V_{th}^2 / (4 \times R_{th})$.
function calculateThevenin() {
var voc = document.getElementById('thev_voc').value;
var isc = document.getElementById('thev_isc').value;
var errorDiv = document.getElementById('thev_error');
var resultBox = document.getElementById('thev_result_box');
var v = parseFloat(voc);
var i = parseFloat(isc);
// Reset displays
errorDiv.style.display = 'none';
resultBox.style.display = 'none';
// Validation
if (isNaN(v) || isNaN(i) || i === 0) {
errorDiv.style.display = 'block';
if (i === 0 && !isNaN(i)) {
errorDiv.innerText = "Short-circuit current cannot be zero (Division by zero).";
} else {
errorDiv.innerText = "Please enter valid numeric values for both fields.";
}
return;
}
if (v < 0 || i < 0) {
errorDiv.style.display = 'block';
errorDiv.innerText = "Values should typically be positive for standard DC analysis.";
return;
}
// Calculations
var rth = v / i;
var gth = 1 / rth;
var pmax = (v * v) / (4 * rth);
// Display Results
document.getElementById('res_rth').innerText = rth.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4});
document.getElementById('res_gth').innerText = gth.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 6});
document.getElementById('res_pmax').innerText = pmax.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4});
resultBox.style.display = 'block';
}