Need help with a simple school-task.

Hi!

So, can someone help me with this:

A light-bulb and a resistor is connected in a serie. The resistor is 100 Ohm. And the voltage over the bulb is described as U=I^2/(0.8*10^-3).
If i connect the serie to a 100 Volt DC source, how do i calculate the current and the resistance over the bulb?

A light-bulb and a resistor is connected in a serie. The resistor is 100 Ohm. And the voltage over the bulb is described as U=I^2/(0.8*10^-3).
If i connect the serie to a 100 Volt DC source, how do i calculate the current and the resistance over the bulb?

Click to expand...

Well Let us first analyze the situation. Your problem is illustrated in a picture given below.
It is always better to have a picture to solve the problems,you know.

Here is the representation...


Hope that this picture completely match with your problem.

Now let us start...........

We have applied a 100V dc across the series combination. Let us assume the voltage drop inside the resistor is V_R and voltage drop across the bulb is V_B.

So the total voltage will be V_DC=100V= V_R + V_B

But from Ohm's Law. V_R = I* R = I*100
also from your problem V_B =

U=I²/(0.8*10^-3)

Click to expand...

There fore we will get an equation given below

I²/(0.8*10^-3) + I* 100 = 100 V

Simplifying this, we get
I² + 0.08 I = 0.08 V

Solving this for I, we get

I = .2456571371 & I = - 0.3256571371

Here , it is not wise to assume a negative value for current.
so let us take
I = 0.24566 A
This is the current that flows through the series combination.........
Now your question

how do i calculate the current and the resistance over the bulb?

Click to expand...

see, we got the current, but to find resistance we need the voltage drop across the Bulb.
so
V_B =

U=I²/(0.8*10^-3)

Click to expand...

V_B = .24566²/(0.8*10^-3) = 75.4360445 V
V_R = I*R = .24566*100=24.566V (no need, but just calculated for fun!)
now , By ohm's Law, V=I*R
therefore, R = V/I = 75.4360445/0.24566 = 307.075 ohms.... the resistance offered by the bulb.

thus, your final answers are

Current, I = 0.24566 A
Resistance, R=307.075 ohms