DC circuits (emf, battery power, resistance)

In summary, the conversation discusses the impossibility of a situation where a battery with an emf of 9.2V and an internal resistance of 1.2 ohms is connected to a resistance that extracts a power of 21.2W. The conversation also mentions various equations for voltage, current, and power and suggests finding the conditions for maximum power dissipation in the external resistor.
  • #1
travh2007
2
0

Homework Statement



Why is the following situation impossible? A battery has an emf of E = 9.2V and an internal resistance of r = 1.2 ohms. A resistance R is connected across the battery and extracts from it a power of P = 21.2W.

Homework Equations



My book gives these equations throughout the section:
[tex]\Delta[/tex]V = [tex]\epsilon[/tex] - Ir

[tex]\epsilon[/tex] = IR + Ir

I = [tex]\epsilon[/tex]/(R+r)

P=I[tex]\Delta[/tex]V

The Attempt at a Solution



I tried plugging in some of my values into some of these formulas, but I don't know the current, so therefore any formula with I in it, I couldn't do. Can someone steer me in the correct direction somehow please?
 
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  • #2
Presumably they mean that the external resistor is to dissipate 21.2W .

Here are some additional relationships for power that you might find useful in your career:

P = I*V = I2R = V2/R

You should be able to write an expression for the power dissipated in the external resistor given its value, and determine the conditions for maximum possible dissipation.
 

FAQ: DC circuits (emf, battery power, resistance)

What is the difference between EMF and voltage?

EMF (electromotive force) is the energy per unit charge that a source (such as a battery) can provide to an electric circuit. Voltage, on the other hand, is the potential difference between two points in a circuit that allows the flow of electric current. In other words, EMF is the driving force behind the flow of current, while voltage is the measure of this flow.

How does a battery produce electricity?

A battery produces electricity through a chemical reaction that generates an excess of electrons at the negative terminal and a deficiency of electrons at the positive terminal. This creates a potential difference between the two terminals, which drives the flow of electrons through a circuit.

What is the relationship between resistance and current in a DC circuit?

According to Ohm's Law, the relationship between resistance (R), current (I), and voltage (V) in a DC circuit is given by the equation V = IR. This means that as resistance increases, the current decreases and vice versa. In other words, the higher the resistance in a circuit, the more difficult it is for current to flow through it.

How do you calculate the power of a battery in a DC circuit?

The power of a battery in a DC circuit can be calculated using the equation P = IV, where P represents power, I represents current, and V represents voltage. This means that the power of a battery is directly proportional to the current and voltage in the circuit. The unit of power is watts (W).

What happens to the voltage in a circuit when more batteries are added?

When more batteries are added to a circuit, the total voltage increases. This is because the voltage of each battery adds up to create a larger potential difference. For example, if two 1.5V batteries are connected in series, the total voltage in the circuit will be 3V. However, the current remains the same as the voltage does not affect the flow of electrons in the circuit.

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