Copper winding

Calculate the current flowing through the copper winding at an operating temperature of 70°C. Celsius, if the winding diameter is 1.128 mm and the winding length is 40 m. The winding is connected to 8V.

Correct result:

I =  9.5174 A

Solution:

$$\begin{gathered} U=8\text{ V } \\ D=1.128\text{ mm}\to \text{ m}=1.128\mathrm{/}1000\text{ m}=0.00113\text{ m } \\ l=40\text{ m } \\ {t}_1=20^{\circ }\text{C } \\ {t}_2=70^{\circ }\text{C } \\ t=t_2-t_1=70-20=50^{\circ }\text{C } \\ \alpha =0.004 \\ {\rho }_0=1.75\cdot 10^{-8}\doteq 1.75\cdot 10^{-8}\mathrm{\Omega } \\ \rho ={\rho }_0\cdot (1+\alpha \cdot t)=1.75\cdot 10^{-8}\cdot (1+0.004\cdot 50)\doteq 2.1\cdot 10^{-8}\mathrm{\Omega } \\ r=D\mathrm{/}2=0.0011\mathrm{/}2\doteq 0.0006\text{ m } \\ S=\pi \cdot r^2=3.1416\cdot 0.0006^2\doteq 9.9933\cdot 10^{-7}{\text{m}}^2 \\ R=\rho \cdot {\displaystyle \frac{l}{S}}=2.1\cdot 10^{-8}\cdot {\displaystyle \frac{40}{9.9933\cdot 10^{-7}}}\doteq 0.8406\mathrm{\Omega } \\ I={\displaystyle \frac{U}{R}}={\displaystyle \frac{8}{0.8406}}=9.5174\text{ A} \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Mains voltage
  How much electric current flows through the appliance with a resistance of 40kΩ, which is connected to the mains voltage (230 V)?
• Copper Cu wire
  Copper wire with a diameter of 1 mm and a weight of 350 g is wound on a spool. Calculate its length if the copper density is p = 8.9 g/cm cubic.
• Current in the conductor
  Calculate the current in the conductor (in mA) if it is connected to a 4.5 V voltage source and its resistance is 20 (ohm).
• The copper wire
  The copper wire bundle with a diameter of 2.8mm has a weight of 5kg. How many meters of wire is bundled if 1m3 of copper weighs 8930kg?
• Filament of bulb
  The filament of bulb has a 1 ohm resistivity and is connected to a voltage 220 V. How much electric charge will pass through the fiber when the electric current passes for 10 seconds?
• Electrics - conductor
  The wire is 106 meters long at 0 °C and at every temperature increase of 1 °C the length increases by 0.15 mm per 1 m length of wire. Determine a function which represents the overall length of the wire as a function of temperature. What is the length of
• Two resistors
  Two resistors 20 Ω and 60 Ω are connected in series and an external voltage of 400 V is connected to them. What are the electrical voltages on the respective resistors? Please comment!
• Resistance
  Determine the resistance of the bulb with the current 200 mA and is in a regular lamp (230V).
• Resistance of the resistor
  The resistor terminals have a voltage of 20 V and a current of 5 mA is passed through. What is the resistance of the resistor?
• Winch
  The steel rope has a diameter of 6mm and a length of 20m. We are winding on drum width 60mm, starting diameter 50mm. What is the final diameter after winding?
• The bulb
  What is the resistance of a filament lamp when it is connected to a 9V battery and has a current of 120 mA?
• The coil
  How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
• Lowest voltage
  Three resistors with resistors R1 = 10 kΩ, R2 = 20 kΩ, R3 = 30 kΩ are connected in series and an external voltage U = 30 V is connected to them. On which resistor is the lowest voltage?
• Coil as a girl
  The electrical resistance of the copper wire coil is 2.0 ohms. What current runs through the coil when the voltage between the terminals is 3.0 V?
• Copper wire
  What is the weight of 1000 m copper wire with a diameter of 5 mm when metric density p = 8.8 g/cm³?
• Cu wire
  Copper wire has a length l = 980 m and diameter d = 8 mm. Calculate the weight if density of copper is ρ = 8500 kg/m³. Result round to one decimal place.
• Iron density
  Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3.