Calculate the terminal voltage for a battery with an internal resistance of 0.900 Ω and an emf of 6.00 V when the battery is connected in series with a 61.0-Ω resistor.

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Identify the key variables in the problem: the internal resistance of the battery \( r = 0.900 \, \Omega \), the emf of the battery \( \text{emf} = 6.00 \, \text{V} \), and the external resistance \( R = 61.0 \, \Omega \). The goal is to calculate the terminal voltage \( V_{\text{terminal}} \).

Recall the formula for terminal voltage: \( V_{\text{terminal}} = \text{emf} - I r \), where \( I \) is the current flowing through the circuit. To find \( I \), use Ohm's Law: \( I = \frac{\text{emf}}{R + r} \).

Substitute the given values into the current formula: \( I = \frac{6.00}{61.0 + 0.900} \). Simplify the denominator to find the total resistance \( R_{\text{total}} = R + r \).

Once \( I \) is calculated, substitute it back into the terminal voltage formula: \( V_{\text{terminal}} = 6.00 - I \cdot 0.900 \).

Simplify the expression to find the terminal voltage. Ensure units are consistent throughout the calculation, and the final answer will be in volts (V).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electromotive Force (emf)

Electromotive force (emf) is the voltage generated by a battery or other energy source when no current is flowing. It represents the maximum potential difference the source can provide. In this context, the emf of 6.00 V indicates the ideal voltage output of the battery under open-circuit conditions.

Internal Resistance

Internal resistance refers to the opposition to current flow within the battery itself, which can affect the actual voltage output when the battery is in use. In this case, the internal resistance of 0.900 Ω will cause a voltage drop when current flows, reducing the terminal voltage available to external components.

Terminal Voltage

Terminal voltage is the voltage output of a battery when it is connected to a load and current is flowing. It can be calculated by subtracting the voltage drop across the internal resistance from the emf. This concept is crucial for understanding how the battery performs under load conditions, such as when connected to a resistor.