Respuesta :
Answer:
The power input and output of the transformer should be the same. That is exactly how we derive the transformer equations.
Explanation:
The main transformer equation relating the turn ratios, the voltages and the currents is as given below.
[tex]N_{p} /N_{s} = V_{p} /V_{s} = I_{s} /I_{p}[/tex]
We got the third part of the equation by appreciating that input power and the output power of the transformer are equal. That is,
[tex]P_{s} = P_{p}[/tex].
[tex]P_{s} = I_{s} V_{s} =P_{p} = I_{p} V_{p}[/tex]
Using this fact exactly we get,
[tex]V_{p} = P_{p} /I_{p} \\and \\V_{s} = P_{s} /I_{s}[/tex]
which we plug in the second equality of the first equation to obtain the third equality of the first equation. So the input and the output powers of the transformers are the same. If we were given a value for the input current we could have calculated the output current by using the first equation since we have available both turn ratios and then we could have used the third equation to calculate the power, where the secondary voltage is given by,
[tex]V_{s} = V_{p} N_{s} /N_{p} = 3300/7 V[/tex].
In actuality there are always some losses in the core of the transformer and due to the resistance and inductance of the wire making up the coil , due to which the output power would be somewhat less than the input power, but we need not concern ourselves too much with that since we cannot hope to calculate that because we don't have the relevant data available.
Step up transformer has 350 turns on the primary coil and 1500 turns secondary coil has input power of the transformer is 21.15 ([tex]I_i[/tex]) Watt output power 88.85 ([tex]I_o[/tex]) Watt.
What is the power of transformer?
The primary winding of the transformer converts the electric power into the magnetic power and the secondary winding of the transformer converts it back into the required electric power.
The ratio of the input voltage to the output voltage is equal to the ratio of number of turns of primary winding to the number of turns of secondary winding. Thus,
[tex]\dfrac{V_i}{V_o}=\dfrac{N_p}{N_s}[/tex]
Given information-
The number of turns in the primary coil of transformer is 350.
The number of turns in the secondary coil of transformer is 1500.
The potential difference between the coil is 110 V.
Put the value in the above formula as,
[tex]\dfrac{V_i}{110-V_i}=\dfrac{350}{1500}[/tex]
[tex]V_i=21.15[/tex]
Thus,
[tex]V_o=110-21.15[/tex]
V(o)=88.85
Thus the input voltage is 21.15 volts and output voltage is 88.85 volts.
Let the value of current is I. As the electric power is the product of current and the voltage.
In the step up transformer the voltage of secondary winding is more then the primary winding but the power remain same.
Thus input power of the transformer is,
P(i)=21.15 ([tex]I_i[/tex]) Watt
The output power of the transformer is,
P(o)=88.85 ([tex]I_o[/tex]) Watt
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