# Solved: Power & Batteries Calc: Resistance, Factor Increase

• mer584
In summary, the resistance of the bulb in an ordinary flashlight is calculated to be 3.33 ohms and the power dissipated is 1.4W. When 4 D-cell batteries are used in series with the same bulb, the power increases by a factor of 4 due to the increase in voltage across the bulb.
mer584

## Homework Statement

An Ordinary flashlight uses two D-cell 1.5V batteries connected in series. The bulb draws 450mA when turned on. A)Calculate the resistance of the bulb and the power dissipated. B) By what factor would the power increase if 4 D-cell batteries in series were used with the same bulb? (neglect heating effects)

## Homework Equations

P=IV=I^2R=V^2/R V=IR

## The Attempt at a Solution

I understand part A, and I got 1.4W for the power. For part B though, I keep getting that it's 2 times greater by doing P=IV where (.45A)(4 x 1.5) =2.7. but I know the answer is supposed to be 4 times. I'm pretty sure the current stays constant and that you add voltages, so I'm confused why it would be 4 and not 2.

Any help would be appreciated!

You are correct in thinking that the current stays constant and that the voltage increases when batteries are connected in series. However, remember that power is also dependent on voltage and resistance. In this case, the resistance of the bulb remains the same, but the voltage across it increases when more batteries are added in series.

Using the equation P=V^2/R, we can see that the power is directly proportional to the square of the voltage. So, when 4 D-cell batteries are used in series, the voltage across the bulb would be (4 x 1.5V) = 6V. Plugging this into the equation, we get P=(6V)^2/R=4P, where P is the power dissipated by the bulb with 2 D-cell batteries.

Therefore, the power would increase by a factor of 4 when 4 D-cell batteries are used in series with the same bulb. I hope this helps clarify your confusion. Keep up the good work!

I would like to clarify that the power dissipated in a circuit is directly proportional to the voltage and the current, and is not affected by the number of batteries in series. Therefore, the power dissipated in the circuit with 4 D-cell batteries in series would still be 1.4W, the same as in the circuit with 2 D-cell batteries in series. The factor by which the power would increase is actually 2, not 4. This can be seen by using the equation P=V^2/R, where the voltage would increase by a factor of 2 (from 3V to 6V) and the resistance would remain the same, resulting in a factor of 2 for the power increase. It is important to note that this calculation neglects any heating effects from the increased voltage, which may affect the actual power dissipated in the circuit.

## 1. What is the purpose of the "Power & Batteries Calc"?

The purpose of the "Power & Batteries Calc" is to calculate the resistance and factor increase in a circuit, in order to determine the power and battery requirements for a specific electronic device or system.

## 2. How does the calculator determine resistance?

The calculator determines resistance by using Ohm's Law, which states that resistance is equal to the voltage divided by the current in a circuit. The calculator takes into account the voltage and current values that are entered and calculates the resistance accordingly.

## 3. What is the factor increase and why is it important?

The factor increase is a measure of how much the power requirement increases when the resistance in a circuit increases. It is important because it helps determine the appropriate battery size and power source needed to provide enough energy to the circuit.

## 4. How accurate is the calculator's results?

The calculator's results are highly accurate, as it uses precise mathematical calculations based on established laws and principles in electrical engineering. However, it is important to note that the accuracy of the results also depends on the accuracy of the input values.

## 5. Can the calculator be used for all types of circuits?

Yes, the calculator can be used for a variety of circuits, including series, parallel, and complex circuits. However, it is important to note that the calculator may not account for all factors in every circuit, so it is always recommended to double check the results with other sources or consult a professional for more complex circuits.

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