a resistor in series with an 8 ohm resistor absorbs 100w when the two are connected across a 60v power supply. find the unknown resistance R.
help with working through the question would be a major help please.
help with working through the question would be a major help please.
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Well, let's see. The overall resistance is R + 8.
We know 100 W = P = I^2 * 8 is the power in the 8 ohm resistor.
And we know I = 60/(R + 8) using Ohm's Law.
So 100 = 60^2 * 8/(R + 8)^2
You can rearrange that to solve for (R + 8), then subtract 8.
Edit: Sorry, that 100 W is in the unknown resistor.
100 = I^2/R = 60^2/[(R+8)^2 R]
The equation isn't so simple. I have to think about this to see if there's a simpler approach.
We know 100 W = P = I^2 * 8 is the power in the 8 ohm resistor.
And we know I = 60/(R + 8) using Ohm's Law.
So 100 = 60^2 * 8/(R + 8)^2
You can rearrange that to solve for (R + 8), then subtract 8.
Edit: Sorry, that 100 W is in the unknown resistor.
100 = I^2/R = 60^2/[(R+8)^2 R]
The equation isn't so simple. I have to think about this to see if there's a simpler approach.
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the problem is you need two equations to solve this.
first v=ir volts = current (amps) X resistance (ohms)
as you dont know the current in amps that is the first to be resolved.
P = VI power = volts times current
therefor P divided by V = current so 100watt divided bt 60 volts = 1. 666666666r
V= IR so V divided by I = total resistance of the circuit
60 divided by 1.66666666r is 36 ohms total
36 ohms minus 8 ohms the resistor in series is 28 ohms
the r after 1.6666666 means recurring
first v=ir volts = current (amps) X resistance (ohms)
as you dont know the current in amps that is the first to be resolved.
P = VI power = volts times current
therefor P divided by V = current so 100watt divided bt 60 volts = 1. 666666666r
V= IR so V divided by I = total resistance of the circuit
60 divided by 1.66666666r is 36 ohms total
36 ohms minus 8 ohms the resistor in series is 28 ohms
the r after 1.6666666 means recurring