A transformer with 360 turns in its primary coil and 18 turns in its secondary coil is designed to delivered an average power of 1400 W with a maximum voltage of 60 V. What is the maximum current in the primary coil?
The primary coil has 360/18 = 20 times the voltage of the secondary coil. It also has 1/20 the current.
The max current in the secondary circuit is sqrt2*rms current = 1.414*1400/60 = 33.0 A
In the primary coil, multiply that number by 20.
To find the maximum current in the primary coil of the transformer, we can use the formula:
\(P_{\text{primary}} = V_{\text{primary}} \times I_{\text{primary}}\)
where \(P_{\text{primary}}\) is the power in the primary coil, \(V_{\text{primary}}\) is the voltage in the primary coil, and \(I_{\text{primary}}\) is the current in the primary coil.
Given that \(P_{\text{primary}} = 1400\) W and \(V_{\text{primary}} = 60\) V, we can rearrange the formula to solve for \(I_{\text{primary}}\):
\(I_{\text{primary}} = \frac{P_{\text{primary}}}{V_{\text{primary}}}\)
Substituting the given values:
\(I_{\text{primary}} = \frac{1400\, \text{W}}{60\, \text{V}}\)
Now we need to determine the turns ratio of the transformer to relate the current in the primary coil to the current in the secondary coil. The turns ratio is given by:
\(\text{Turns ratio} = \frac{\text{Number of turns in primary coil}}{\text{Number of turns in secondary coil}}\)
In this case, the number of turns in the primary coil is 360, and the number of turns in the secondary coil is 18. Plugging in these values:
\(\text{Turns ratio} = \frac{360}{18} = 20\)
The current in the secondary coil can be found using the turns ratio:
\(I_{\text{secondary}} = \frac{I_{\text{primary}}}{\text{Turns ratio}} = \frac{1400\, \text{W}}{60\, \text{V}} \times \frac{1}{20}\)
Simplifying:
\(I_{\text{secondary}} = \frac{1400\, \text{W} \times 1}{60\, \text{V} \times 20}\)
\(I_{\text{secondary}} = \frac{1400}{1200}\, \text{A} \)
\(I_{\text{secondary}} = 1.17\, \text{A} \)
Therefore, the maximum current in the primary coil of the transformer is approximately 1.17 A.