A coil having :

Question

N= 440 turns
diameter =1,2mm
Mean length= 120mm
Inductance= 400micro Henry's
Calculate the resistance is the resistivity of the wire is 0,027micro-ohm meters
Calculate the average value of the EMF induced in a coil when current of 4A is reversed in 0,001 seconds

Answer 1

To solve your problem, we'll tackle it step by step.

Step 1: Calculate the Resistance

To calculate the resistance $R$ of the coil, we can use the formula:

$$R=\rho \frac{L}{A}$$

where:

• $R$ is the resistance,
• $\rho$ is the resistivity of the wire,
• $L$ is the length of the wire,
• $A$ is the cross-sectional area of the wire.

Given values:

• $\rho =0.027,\mu \mathrm{\Omega },m=0.027\times {10}^{-6},\mathrm{\Omega },m$
• Diameter of the wire = 1.2 mm = 0.0012 m
• Mean length $L=120,mm=0.12,m$
• $N=440,turns$

Calculate $A$:

The cross-sectional area $A$ of the wire can be calculated using the formula for the area of a circle:

$$A=\pi {\left(\frac{d}{2}\right)}^2=\pi {\left(\frac{0.0012}{2}\right)}^2$$

Calculating it:

$$A=\pi {\left(0.0006\right)}^2\approx \pi \times 0.00000036\approx 1.131\times {10}^{-6},m^2$$

Calculate $R$:

Now substituting $\rho$, $L$, and $A$ into the resistance formula:

$$R=0.027\times {10}^{-6}\frac{0.12}{1.131\times {10}^{-6}}\approx 0.027\times {10}^{-6}\times 106,272.5$$

Calculating it:

$$R\approx 0.027\times 0.000028707\approx 0.000000773,\mathrm{\Omega }=0.773,\mu \mathrm{\Omega }$$

Step 2: Calculate the Average EMF Induced

The average EMF $\mathcal{E}$ induced in the coil can be calculated using Faraday's law of electromagnetic induction:

$$\mathcal{E}=-L\frac{\mathrm{\Delta }I}{\mathrm{\Delta }t}$$

Where:

• $L$ is the inductance (in henries),
• $\mathrm{\Delta }I$ is the change in current,
• $\mathrm{\Delta }t$ is the change in time.

Given values:

• $L=400,\mu H=400\times {10}^{-6},H$
• Change in current $\mathrm{\Delta }I=4A-(-4A)=4A+4A=8A$
• Change in time $\mathrm{\Delta }t=0.001,s$

Calculate $\mathcal{E}$:

Substituting the values:

$$\mathcal{E}=-400\times {10}^{-6}\frac{8}{0.001}$$

Calculating it:

$$\mathcal{E}=-400\times {10}^{-6}\times 8000=-3.2,V$$

Thus, the average value of the EMF induced in the coil is approximately 3.2 V (the negative sign indicates the direction of induced EMF opposing the change in current).

Final Results:

• Resistance of the coil: $R\approx 0.773,\mu \mathrm{\Omega }$
• Average EMF induced: $|\mathcal{E}|\approx 3.2,V$