Find transformer primary and secondary voltage/current

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In summary: You need an app to solve an equation in one unknown?? :wink:Two unknowns. But when we only have 50 minutes for an exam, I need to find one that doesn't break my calculator!
  • #1
Bluestribute
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Homework Statement


(in picture)

Homework Equations


V=IZ
All the ratio formulas (i.e. V2/V1 = N2/N1)

The Attempt at a Solution


I thought V1 would be 1000 Vrms. Well the answers are shown and it's not. So I thought maybe I would multiply Vrms (1000) by root 2 to find Vpeak (Vrms = Vpeak/root 2). Didn't work. I know if I find V1, the rest will fall into place because from there, it's simple ratios. But it's getting the answer of 790.6cos(18.43) that I'm having trouble with . . .
 

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  • #2
V1 is not 1000V because some of Vs is lost in the 1000 ohm series resistance, by Ohms Law.
 
  • #3
Right. But there's only one resistor, so the voltage always comes out to 1000. I tried doing voltage division this way:

V1 = (Vs(RL+XL))/(1010 + j20)

And didn't get the correct result either. I used the (10 + j20) combination as the load in my division.
 
  • #4
You need to have an expression for the current in order to determine how much of Vs is lost across that series resistance. So what is an expression for the primary current in terms of other parameters?
 
  • #5
As far as we can tell from the problem statement the transformer is ideal and has a 10:1 turns ratio. What does that tell us about the relationships between V1 and V2, I1 and I2?
 
  • #6
NascentOxygen said:
You need to have an expression for the current in order to determine how much of Vs is lost across that series resistance. So what is an expression for the primary current in terms of other parameters?
Um . . . I don't know . . .

gneill said:
As far as we can tell from the problem statement the transformer is ideal and has a 10:1 turns ratio. What does that tell us about the relationships between V1 and V2, I1 and I2?

I know the ratio (V1/V2 = N1/N2, and inverse for current), but I need the V1 first . . .
 
  • #7
Bluestribute said:
I know the ratio (V1/V2 = N1/N2, and inverse for current), but I need the V1 first . . .
That's why you need to write loop equations (KVL). The now known relationships between V1 and V2, I1 and I2, allows you to eliminate two of the variables, leaving two equations in two unknowns.
 
  • #8
You can often start on the secondary side, and work back towards the primary.
 
  • #9
NascentOxygen said:
You can often start on the secondary side, and work back towards the primary.
Go on . . . Because I thought of that but have no voltage or current to use.

gneill said:
That's why you need to write loop equations (KVL). The now known relationships between V1 and V2, I1 and I2, allows you to eliminate two of the variables, leaving two equations in two unknowns.
1000 + 1000I1 +V1 = 0
(10 + j20)I2 - V2 = 0

V1/V2 = I2/I1

These the equations you're referring to?
 
  • #10
Bluestribute said:
1000 + 1000I1 +V1 = 0
(10 + j20)I2 - V2 = 0

V1/V2 = I2/I1

These the equations you're referring to?
Almost. The first equation is not correct. Check the signs of the terms.

And you are given the transformer turns ratio, so use it.
 
  • #11
-1000 + 1000(I1) + V1 = 0
(10 + j20)I2 - V2 = 0

I2/I1 = 10 (Or N1/N2 if you'd prefer).

So I can turn I2 into 10I1 and V2 into 0.1V1?
 
  • #12
Bluestribute said:
-1000 + 1000(I1) + V1 = 0
(10 + j20)I2 - V2 = 0

I2/I1 = 10 (Or N1/N2 if you'd prefer).

So I can turn I2 into 10I1 and V2 into 0.1V1?
Yup.
 
  • #13
Boom. Took forever to find a Ti-84 App to do the trick but got one. Did not think you had to do that with such a simple transformer setup.
 
  • #14
Bluestribute said:
Boom. Took forever to find a Ti-84 App to do the trick but got one. Did not think you had to do that with such a simple transformer setup.
You need an app to solve an equation in one unknown?? :wink:
 
  • #15
Two unknowns. But when we only have 50 minutes for an exam, I need to find one that doesn't break my calculator! AHHH.
 

1. How do I calculate the primary voltage and current of a transformer?

The primary voltage and current of a transformer can be calculated by using the transformer's turns ratio and the secondary voltage and current. The formula for calculating the primary voltage is Vp = Vs(Np/Ns), where Vp is the primary voltage, Vs is the secondary voltage, Np is the number of turns in the primary coil, and Ns is the number of turns in the secondary coil. The formula for calculating the primary current is Ip = Is(Ns/Np), where Ip is the primary current, Is is the secondary current, Np is the number of turns in the primary coil, and Ns is the number of turns in the secondary coil.

2. How do I determine the turns ratio of a transformer?

The turns ratio of a transformer can be determined by dividing the number of turns in the secondary coil by the number of turns in the primary coil. This ratio is also known as the voltage ratio, as it is the same as the ratio of the secondary voltage to the primary voltage.

3. Can I find the primary and secondary voltage and current of a transformer by measuring them?

Yes, the primary and secondary voltage and current of a transformer can be measured using a multimeter. To measure the voltage, set the multimeter to the AC voltage setting and place the probes across the primary or secondary terminals. To measure the current, set the multimeter to the AC current setting and place the probes in series with the primary or secondary circuit.

4. How do I know the primary and secondary voltage and current of a transformer if I don't have access to the transformer's specifications?

If you do not have access to the transformer's specifications, you can determine the primary and secondary voltage and current by performing a load test. This involves connecting a known load to the secondary side of the transformer and measuring the resulting voltage and current. Using the turns ratio, you can then calculate the primary voltage and current.

5. How do I choose the appropriate transformer for my application?

The appropriate transformer for your application will depend on the required voltage and current specifications. You will also need to consider factors such as the transformer's power rating, frequency, and physical size. It is best to consult with a qualified electrician or engineer to ensure you select the correct transformer for your specific needs.

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