Question

A voltaic cell provides a current of 0.5 A when in a circuit with a 3 ? resistor. If the internal resistance of the cell is 0.1 ?, what is the voltage across the terminals of the battery when there is no current flowing? (A) 0.05 V (B) 1.5 V (C) 1.505 V (D) 1.55 V

Short answer

1.55 V

Step-by-step solution

- Find Total Resistance

Add the internal resistance of the cell to the external resistance. The total resistance is given by: \[ R_{total} = R_{external} + R_{internal} = 3 \Omega + 0.1 \Omega = 3.1 \Omega \]

- Calculate Total Voltage

Using Ohm's law, calculate the total voltage across the circuit: \[ V_{total} = I \times R_{total} = 0.5 \text{ A} \times 3.1 \Omega = 1.55 \text{ V} \]

- Determine Voltage with No Current

When no current is flowing, the voltage across the terminals is the same as the total voltage. Therefore, the voltage across the terminals is: \[ V_{terminal} = 1.55 \text{ V} \]

Key concepts

Ohm's Law

Ohm's Law is a fundamental principle in physics and electrical engineering. It states that the voltage (\textbf{V}) across a conductor is proportional to the current (\textbf{I}) flowing through it, with the constant of proportionality being the resistance (\textbf{R}) of the conductor. Mathematically, it is expressed as:
\[ V = I \times R \]
Understanding Ohm's Law is crucial for solving electrical circuits and analyzing how different elements interact. In the context of the given exercise, Ohm's Law helps calculate the total voltage in the circuit, taking into consideration the current supplied by the cell and the total resistance due to both the internal and external resistances.

Internal resistance

Internal resistance is the inherent resistance to the flow of current within the components of a power source, such as a battery or voltaic cell. It affects the overall performance of the power source and needs to be accounted for in calculations.

• Determining internal resistance: It is usually given or can be found through experiments.
• Impact on total resistance: Adding internal resistance to external resistance affects the total resistance in the circuit. As illustrated in the given problem, the combined resistance becomes the sum of the internal resistance and the external resistor's resistance:

\[ R_{total} = R_{external} + R_{internal} \]
In our example, this total resistance was found to be 3.1 \Omega. By acknowledging the internal resistance, you ensure that voltage and current calculations reflect the real-world scenario accurately.

Electrochemistry

Electrochemistry involves the study of chemical processes that cause electrons to move, which is fundamentally how electricity is generated by voltaic cells and batteries.
Voltaic cells, also known as galvanic cells, convert chemical energy into electrical energy through redox reactions. A standard voltaic cell has two electrodes: the anode (oxidation occurs) and the cathode (reduction occurs).
In the given exercise, the voltaic cell generates an electric current by moving electrons through an external circuit. The internal resistance of the cell plays a crucial role in this electron flow, impacting the overall cell voltage when current is flowing.
Calculating the open-circuit voltage (voltage across the terminals with no current) helps determine the cell's true potential. As seen in the exercise, this is equal to the calculated total voltage of 1.55 V when no current flows.