Determine the dielectric constant of slab, Electrical Engineering

Determine the Dielectric constant of slab:

An air capacitor contains two parallel plates 10 cm2 in area and 0.5 cm apart. While a dielectric slab of area 10 cm2 and thickness 0.4 cm was inserted among the plates, one of the plate ought to be shifted by 0.4 cm to attain the same value of capacitance. What is the dielectric constant of slab?

Solution

Capacitance without dielectric slab :

C  = ε0 A / d1= (8.85 × 10 -12 × 10 × 10- 4 ) /0.5 × 10 - 2

= (8.85 × 10-12 ) / 5

Capacitance with dielectric slab :

C2   = (ε0 εr A) /∑ d2     

2368_Determine the Dielectric constant of slab.png

Figure

C2 = (ε0 × 10 × 10- 4)  /((0.5/ εr)+0.4) × 10-2  = ε0/(((5/ εr)+ 4)= (8.85 × 10-12 )/((5/ εr)+ 4)

But

∴ C1 = C2

(8.85 × 10-12 )/((5/ εr)+ 4)= (8.85 × 10-12 )/ 5

∴          εr = 5

1021_Determine the Dielectric constant of slab1.png

Figure

Posted Date: 2/4/2013 5:21:08 AM | Location : United States







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