Calculating Voltage Drop Across a Resistor With Battery Internal Resistance

Understanding how to calculate the voltage drop across a resistor in a circuit that includes a battery's internal resistance is crucial for electrical engineering and physics. This article will walk you through the process using a battery with an electromotive force (EMF) of 40 volts and an internal resistance of 5 ohms, connected to a 15-ohm resistor. By applying Ohm's Law and the overall circuit analysis, you can determine the voltage drop across the resistor.

Given Values

Here are the given values for our calculation:

EMF of the battery (Electromotive Force), E 40 V Internal resistance of the battery, r 5 Ω Resistance of the external resistor, R 15 Ω

Total Resistance and Current in the Circuit

To begin, we need to find the total resistance in the circuit. The total resistance is the sum of the internal resistance and the external resistance.

Total Resistance:

Rtotal r R 5 Ω 15 Ω 20 Ω

Now, let's calculate the current flowing through the circuit using Ohm's Law:

Circuit Current:

I E / Rtotal 40 V / 20 Ω 2 A

Voltage Drop Across the Resistor

To find the voltage drop across the 15-ohm resistor, we can use Ohm's Law again:

Voltage Drop Across the Resistor R:

VR I × R 2 A × 15 Ω 30 V

Conclusion

The voltage drop across the 15-ohm resistor is 30 volts.

Total Circuit Resistance

The total resistance in the circuit is the sum of the internal resistance and the external resistance:

Rtotal 5 Ω 15 Ω 20 Ω

Circuit Current

The current through the circuit can be calculated as:

I E / Rtotal 40 V / 20 Ω 2 A

Drop Across the 15Ω Resistor

The voltage drop across the 15-ohm resistor is:

V I × R 2 A × 15 Ω 30 V

Total Resistance and Current Using EMF

The total resistance in the circuit is 20 ohms. The current flowing through the circuit is 2 amps. The voltage drop across the 15-ohm resistor is:

V I × R 2 A × 15 Ω 30 V

It's important to note that the EMF (electromotive force) of the battery is 40 volts when no current is flowing through the cell. When current flows, including the internal resistance, the total resistance is 20 ohms, and the current is 2 amps.