Math Problem Statement
Calculate the terminal voltage for a battery with an internal resistance of 0.685 Ω and an emf of 4.25 V when the battery is connected in series with an 77.6 Ω resistor.
Solution
To calculate the terminal voltage () of the battery, we use the following formula:
where:
- is the electromotive force of the battery (),
- is the current in the circuit,
- is the internal resistance of the battery ().
Step 1: Calculate the total resistance of the circuit
The total resistance is the sum of the internal resistance of the battery and the resistance of the external resistor :
Step 2: Calculate the current in the circuit
Using Ohm's law (), the current is:
Step 3: Calculate the terminal voltage
The terminal voltage is then calculated as:
Substituting the values:
Final Answer:
The terminal voltage of the battery is approximately 4.21 V.
Would you like further clarifications or have more related questions? Here are some related topics you might explore:
- How does increasing the internal resistance affect the terminal voltage?
- What happens to the current if the external resistance is reduced?
- Can you calculate power dissipated in the external resistor?
- How is terminal voltage related to energy loss within the battery?
- What would happen if the external resistor is replaced with a short circuit?
Tip: Always check the units for resistance, current, and voltage to ensure consistency in calculations.
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Math Problem Analysis
Mathematical Concepts
Ohm's Law
Series Circuits
Voltage Drop
Formulas
V_terminal = emf - I * r
I = emf / R_total
R_total = r + R
Theorems
Ohm's Law
Suitable Grade Level
Grades 9-12
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