Internal Resistance of a Battery, EMF, Cell Terminal Voltage, Physics Problems
TLDRThis video script explains the concept of calculating a battery's internal resistance and terminal voltage. It introduces the relationship between a battery's electromotive force (EMF), terminal voltage (VR), and the impact of load resistance on current and voltage drop. The script provides a step-by-step guide on how to calculate terminal voltage with different load resistances and how to determine a battery's internal resistance using measured terminal voltage and Ohm's law. The examples given illustrate the significant voltage drop when a battery is connected to a low-resistance device due to increased current draw.
Takeaways
- 🔋 The video explains how to calculate a battery's internal resistance and terminal voltage.
- 🔌 Internal resistance (r) is represented in a circuit diagram along with the battery and affects the terminal voltage (VR).
- 💡 The electromotive force (EMF) is the actual internal voltage of the battery, which may differ from the terminal voltage read on a device.
- 📉 Terminal voltage decreases as the current (I) drawn from the battery increases, contrary to the expectation from Ohm's law (V=IR).
- 🔍 To calculate terminal voltage (VR), find the equivalent resistance of the circuit (R + r) and use Ohm's law (EMF/R) to determine the current (I).
- 🔎 For a high load resistance (R), the current drawn is smaller, leading to a minimal voltage drop and a terminal voltage close to the EMF.
- 🌡️ When the load resistance is low, more current is drawn, resulting in a significant voltage drop and a lower terminal voltage.
- 🔄 The video provides an example calculation for a battery with 12V EMF, 0.1 ohm internal resistance, and load resistances of 1 ohm and 100 ohms.
- 📊 It demonstrates that with a 1-ohm load, the terminal voltage is 10.91V, and with a 100-ohm load, it is 11.988V.
- 🔧 The process of finding the internal resistance involves measuring the terminal voltage across a known load resistance and solving the equation for r using the known EMF, current, and terminal voltage.
Q & A
What is the internal resistance of a battery and why is it important?
-The internal resistance of a battery, denoted by the symbol 'r', is the resistance within the battery itself that can affect the efficiency of energy transfer. It is important because it causes a voltage drop across the battery as current flows, resulting in a terminal voltage that is lower than the electromotive force (EMF) of the battery.
What is the difference between EMF and terminal voltage?
-EMF (electromotive force) is the actual internal voltage of the battery, which is the energy per unit charge provided by the battery. Terminal voltage, on the other hand, is the voltage that is read when the battery is connected to a device. Terminal voltage is usually lower than EMF due to the voltage drop caused by the internal resistance of the battery and the resistance of the device.
How does the terminal voltage change with the load resistance?
-As the load resistance decreases, more current is drawn from the battery, leading to a greater voltage drop across the internal resistance of the battery. This results in a lower terminal voltage. Conversely, with a higher load resistance, less current is drawn, causing a smaller voltage drop and a terminal voltage closer to the EMF of the battery.
What is the formula to calculate the terminal voltage?
-The terminal voltage (Vr) can be calculated using the formula: Vr = EMF - Ir, where EMF is the electromotive force of the battery, I is the current flowing through the circuit, and r is the internal resistance of the battery.
How can you calculate the internal resistance of a battery if you know the EMF, terminal voltage, and load resistance?
-You can calculate the internal resistance (r) of a battery using the formula: r = (EMF - Vr) / I, where EMF is the electromotive force, Vr is the terminal voltage, and I is the current flowing through the circuit, which can be determined by Ohm's law (V = IR).
What happens to the terminal voltage when the load resistance is very high?
-When the load resistance is very high, the current drawn from the battery is minimal. As a result, the voltage drop across the internal resistance is small, and the terminal voltage is close to the EMF of the battery.
How does the current flowing through the circuit affect the terminal voltage?
-The terminal voltage decreases as the current flowing through the circuit increases. This is because a higher current results in a greater voltage drop across the internal resistance of the battery, leading to a lower terminal voltage.
What is the equivalent resistance when two resistors are connected in series?
-The equivalent resistance (total resistance) of two resistors connected in series is simply the sum of their individual resistances, calculated as R_total = R1 + R2.
How can you find the current flowing through a circuit?
-The current (I) flowing through a circuit can be found using Ohm's law, which states I = V / R, where V is the voltage (EMF) and R is the total resistance of the circuit.
What is the relationship between the terminal voltage and the load resistor's resistance?
-The terminal voltage is directly related to the load resistor's resistance. As the load resistance increases, the current drawn from the battery decreases, leading to a smaller voltage drop and a higher terminal voltage. Conversely, a lower load resistance results in a higher current and a larger voltage drop, causing a lower terminal voltage.
How can you measure the terminal voltage across a resistor?
-The terminal voltage across a resistor can be measured using a voltmeter. When the voltmeter is connected across the resistor, it reads the voltage, which is the terminal voltage of the battery in that circuit.
What are the steps to calculate the internal resistance of a battery given the EMF, load resistance, and terminal voltage?
-First, measure the terminal voltage across the load resistor with a voltmeter. Then, calculate the current flowing through the circuit using Ohm's law (I = Vr / R_load). Finally, use the formula for terminal voltage (Vr = EMF - Ir) to solve for the internal resistance (r = (EMF - Vr) / I).
Outlines
🔋 Understanding Battery Internal Resistance and Terminal Voltage
This paragraph introduces the concept of calculating a battery's internal resistance and terminal voltage. It explains that the terminal voltage (vr) is not always the same as the electromotive force (emf) due to the battery's internal resistance (r). The paragraph details a method to calculate terminal voltage by first finding the equivalent resistance of a series circuit, then determining the current through the circuit, and finally using Ohm's law to calculate the terminal voltage (Vr). An example is provided using a 12-volt battery with 0.1 ohms internal resistance and load resistances of 1 ohm and 100 ohms to illustrate how the terminal voltage decreases as the current increases.
📈 Calculating Terminal Voltage with Varying Load Resistance
This paragraph focuses on the impact of load resistance on terminal voltage. It explains how the equivalent resistance is calculated when the load resistance is 1 ohm, and then demonstrates the process of calculating the current and terminal voltage with an example. The paragraph highlights that a higher load resistance results in a smaller current draw and a minimal voltage drop, keeping the terminal voltage close to the emf. Conversely, a lower load resistance leads to a greater current draw and a more significant voltage drop. The paragraph also introduces the concept of calculating the internal resistance of a battery by measuring the terminal voltage across a known load resistor and using the relationship between emf, current, and internal resistance.
🔧 Measuring and Calculating Battery Internal Resistance
The final paragraph delves into the practical steps of measuring and calculating a battery's internal resistance. It outlines the process of first measuring the terminal voltage across a load resistor using a voltmeter, then calculating the current through the circuit. With the current known, the paragraph demonstrates how to solve for the internal resistance using the equation that relates the terminal voltage to the emf, current, and internal resistance. An example calculation is provided with a 12-volt battery, a 50-ohm load resistor, and a measured terminal voltage of 11.9 volts, leading to the determination of an internal resistance of 0.42 ohms.
Mindmap
Keywords
💡Internal Resistance
💡Terminal Voltage (VR)
💡Electromotive Force (EMF)
💡Load Resistance
💡Ohms Law
💡Voltage Drop
💡Series Circuit
💡Equivalent Resistance
💡Current
💡Circuit Diagram
💡Voltage Measurement
Highlights
The video explains how to calculate the internal resistance and terminal voltage of a battery.
A battery has its own internal resistance, represented by the symbol 'r'.
The electromotive force (EMF) is the actual internal voltage of the battery.
The terminal voltage ('vr') is the voltage read when a battery is connected to a device.
The terminal voltage decreases as the current drawn from the battery increases.
The equivalent resistance of a circuit with series resistors is the sum of the resistances ('r' + 'R').
The current in the circuit is calculated by dividing the EMF by the total resistance.
A high resistance device connected to a battery will draw a small amount of current, leading to a minimal voltage drop.
The terminal voltage can be calculated using the equation 'terminal voltage = current (I) * resistance (r)'.
The voltage drop is significantly greater when the load resistance is low.
The EMF of the battery is 12 volts in the given examples.
The internal resistance of a battery can be calculated if the terminal voltage across a resistor is known.
The current in the circuit is found by using Ohm's law (V = IR).
The internal resistance is calculated using the equation 'terminal voltage = EMF - (current * internal resistance)'.
The internal resistance is 0.42 ohms when the load resistor is 50 ohms and the terminal voltage is 11.9 volts.
The video provides a practical approach to understanding battery characteristics and circuit behavior.
The relationship between current, voltage, and resistance in a battery- resistor circuit is explored.
The impact of varying resistance on terminal voltage and internal resistance is demonstrated.
Transcripts
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