Enter the EMF and resistances. All values will be calculated automatically.

Circuit Current (I)
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Terminal Voltage (V)
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Lost Volts (Ir)
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Power to Load
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Power Wasted
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Efficiency
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Electromotive Force (EMF) vs. Terminal Voltage

Real-world energy sources like batteries are not perfect. They have an inherent internal resistance (r) due to the chemical components or materials they are made of. This leads to a distinction between two types of voltage:

  • EMF (ε): The total energy supplied per unit charge by the source. It is the voltage measured when NO current is flowing (open circuit).
  • Terminal Voltage (V): The actual voltage available to the external circuit when current is flowing. It is always less than the EMF because some energy is "wasted" inside the source.
ε = V + Ir = I(R + r)

"Lost Volts" (Ir)

The term Ir represents the potential difference across the internal resistance. It is often called the "lost volts" because this energy is dissipated as heat within the battery and is not available for the external load.

Lost Volts = ε - V = Ir

Maximum Power Transfer Theorem

A significant concept in both physics exams and engineering: Maximum power is delivered to the external load (R) when the load resistance equals the internal resistance (R = r).

However, at this point, the efficiency is only 50% because half the power is wasted as lost volts inside the source.

Efficiency Calculation:
Efficiency = (Useful Power Out / Total Power In) × 100%
Efficiency = (V / ε) × 100% = (R / (R + r)) × 100%

Worked Examples

✅ Example 1: Calculating Lost Volts

A battery has an EMF of 9.0V. When connected to a bulb, the terminal voltage drops to 8.2V while carrying a current of 0.4A. Calculate the internal resistance.

Step 1: Find lost volts. Lost Volts = ε - V = 9.0 - 8.2 = 0.8V.
Step 2: Use V = Ir. 0.8 = 0.4 × r.
Step 3: Solve for r. r = 0.8 / 0.4 = 2.0Ω

✅ Example 2: Efficiency of a Power Supply

A 12V power supply with 1.5Ω internal resistance is connected to a 10.5Ω resistor. What is the efficiency?

Formula: Efficiency = R / (R + r) × 100%
Calculation: Eff = 10.5 / (10.5 + 1.5) = 10.5 / 12 = 0.875
Result: Efficiency = 87.5%

✅ Example 3: Finding Current

Calculate the current in a circuit with a 1.5V cell (r = 0.1Ω) and a 4.9Ω external resistor.

Total Resistance: Rtot = 4.9 + 0.1 = 5.0Ω.
Current I: I = ε / Rtot = 1.5 / 5.0.
Result: I = 0.3A

✅ Example 4: Maximum Power

A signal generator has an internal resistance of 50Ω. What resistor should be connected to it to receive maximum power, and what is the resulting terminal voltage if ε = 10V?

Matching: For max power, R = r = 50Ω.
Terminal Voltage: Since R=r, the voltage is halved. V = ε/2 = 10/2 = 5.0V.

✅ Example 5: Graphing (Intercept)

For a V-I graph of a battery, the intercept on the V-axis is 12V and the gradient is -2. Identify ε and r.

Analysis: V = ε - Ir can be rewritten as V = (-r)I + ε (y = mx + c form).
Y-Intercept: ε = 12V.
Gradient: -r = -2 → r = 2Ω.