The question is asking what the resistance of the first resistor is (which has been labelled as 0 ohms on the diagram). I am told 20v drops across the first resistor and i am given the value of the other resistor. Now both of the methods I am sure I've done correctly but I'm getting different answers.
In this first method, I simply calculated the current through the 57.6 ohm resistor, which was 220/57.6. To find I1, I would do I3I2. Which is (220/57.6)10 =6.18A. This is the current through the first resistor. Therefore to find its resistance I would do V/I=R.
So it is 20/6.18 = 3.24 Ohms
I was happy with my answer until I decided to try another method, which was to transform the current source into a voltage source and analyse it that way.
To transform to voltage source. I did 10 * 57.6 = 576V. As a current source in parallel with a resistor can be transformed into a voltage source in series with the resistor.
Here I then combined the voltage sources which would be 576240 = 336V
From here I then worked out the current through the 57.6 ohm resistor (which would also be the current through the first resistor). Since 20v is across the first resistor, then 316v would be across the 57.6 ohm resistor. Therefore I = 316/57.6 = 5.4861
Using this value for current, I then used ohms law to work out the resistance of the first resistor. Since R = V/I, I did 20/5.4861 = 3.65 Ohms
Here's my dilemma, both methods seem to be done correctly and should both work to give the same answer, but the first method gives me 3.24 Ohms and the second gives me 3.65 Ohms. I am so confused right now, which method is the correct one and which answer is correct? What did I do wrong.
In this first method, I simply calculated the current through the 57.6 ohm resistor, which was 220/57.6. To find I1, I would do I3I2. Which is (220/57.6)10 =6.18A. This is the current through the first resistor. Therefore to find its resistance I would do V/I=R.
So it is 20/6.18 = 3.24 Ohms
I was happy with my answer until I decided to try another method, which was to transform the current source into a voltage source and analyse it that way.
To transform to voltage source. I did 10 * 57.6 = 576V. As a current source in parallel with a resistor can be transformed into a voltage source in series with the resistor.
Here I then combined the voltage sources which would be 576240 = 336V
From here I then worked out the current through the 57.6 ohm resistor (which would also be the current through the first resistor). Since 20v is across the first resistor, then 316v would be across the 57.6 ohm resistor. Therefore I = 316/57.6 = 5.4861
Using this value for current, I then used ohms law to work out the resistance of the first resistor. Since R = V/I, I did 20/5.4861 = 3.65 Ohms
Here's my dilemma, both methods seem to be done correctly and should both work to give the same answer, but the first method gives me 3.24 Ohms and the second gives me 3.65 Ohms. I am so confused right now, which method is the correct one and which answer is correct? What did I do wrong.
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