How Do You Calculate the Resistance of a Light Bulb in a Series Circuit?

In summary, a light bulb with a 144Ohm resistor is connected in series with a 120.0-V source and delivers 23.4W of power. Using the equations P = I^2R and I = V/R, the resistance of the light bulb can be found by rearranging the equation 23.4(Rb^2 + 288Rb + 144^2) = 120Rb. Simplifying this equation will lead to a quadratic equation in the form ax^2 + bx + c = 0.
  • #1
rcrx
16
0

Homework Statement


A light bulb is wired in series with a 144Ohm resistor, and they are connected across a 120.0-V source. The power delivered to the light bulb is 23.4W. What is ther resistance of the light bulb? Note that there are two possible answers.


Homework Equations


P = I^2R and I = V/R


The Attempt at a Solution


Solve for I to find Rbulb. I = (V / Rb + Rr)^2 x Rb.

Rearranged 23.4(Rb^2 + 288Rb + 144^2) = 120Rb

This is where I'm stuck, I need to rearrange that so I can get ax^2 + bx + c = 0

My math skills are a little weak since I have been out of school for a few years.

Thanks a lot!:smile:
 
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  • #2
Expand the brackets and subtract 120Rb from each side...
 
  • #3
So, pardon me, but I'd get the following?

23.4Rb^2 + (23.4)288Rb + (23.4)144^2 - 120Rb = 0
 
  • #4
rcrx said:
So, pardon me, but I'd get the following?

23.4Rb^2 + (23.4)288Rb + (23.4)144^2 - 120Rb = 0

Yes. Now, since you are dealing with numbers, you can simplify 23.4*288 and subtract 120 to obtain an equation in your required form.
 

FAQ: How Do You Calculate the Resistance of a Light Bulb in a Series Circuit?

What is a quadratic equation?

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It is a type of algebraic equation that involves a squared term and is commonly used to solve problems involving motion, area, and other mathematical concepts.

How do I set up a quadratic equation?

To set up a quadratic equation, first identify the given information or problem and assign variables to represent unknown quantities. Then, use this information to write the equation in the form ax^2 + bx + c = 0. Finally, solve the equation using algebraic techniques such as factoring, the quadratic formula, or completing the square.

What are the key components of a quadratic equation?

The key components of a quadratic equation are the coefficients a, b, and c, which determine the shape and position of the parabola when graphed. The coefficient a represents the quadratic term, b represents the linear term, and c represents the constant term.

What is the difference between a quadratic equation and a linear equation?

A quadratic equation involves a squared term, while a linear equation does not. This means that a quadratic equation will have two solutions, while a linear equation will have just one. Additionally, the graph of a quadratic equation is a parabola, while the graph of a linear equation is a straight line.

How is a quadratic equation used in real life?

Quadratic equations are used in many real-life situations, such as calculating the trajectory of a projectile, determining the minimum or maximum value of a function, and finding the dimensions of a rectangle with a fixed perimeter. They are also used in engineering, physics, and other fields to model various phenomena and make predictions.

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