17 My Notes Ask Your T -3 points SerCP11 16.P.053 voltage across an air-filled p

Question

17 My Notes Ask Your T -3 points SerCP11 16.P.053 voltage across an air-filled parallel-plate capacitor is measured to be 237.0 V. When a dielectric is inserted and completely fills the space ween the plates, as in the figure below, the voltage drops to V2-69.7 V Deleci ? (a) What is the dielectric constant of the inserted material? Can you identify the dielectric? bakelite o neoprene rubber o paper O nylon o teflon (b) If the dielectric doesn't completely fill the space between the plates, what could you conclude about the voltage across the plates? This answer has not been graded yet.

Explanation / Answer

Part (a)

charge in a capacitor, q= CV, where V is the applied voltage and C is the capacitance.

In the given problem, we assume that the charge in the capacitor for both the cases is the same.

q=C1V1=C2V2 (1)

in the first case, V1 = 237.0 V and V2= 69.7 V

now, for a parallel plate capacitor, capacitance, C= ( epsilonr* epsilon0 * A )/d (2)

where epsilonr= dielectric constant of the insulating material

epsilon0 = dielectric constant for air (or vacuum )

A= area of the parallel plates d= separation between the parallel plates

for the first case,  epsilonr =1 and in the second case epsilonr =k (assumed)  

so, from equation (2) , C2/C1= k

from equation (1), C2/C1 = V1/V2

k = (237.0 )/ 69.7 = 3.4.

The dielectric constant of the inserted material is 3.4. (answer)

Among the given options we can find that Nylon has dielectric constant= 3.4. So, the dielectric is nylon (answer).

Part (b)

If the dielectric does not fill the spaces between the plates, there will be two capacitors formed connected in series ( one capacitor with the portion between the plates filled with the dielectric and the other one with the unfilled part). If two capacitors C1 & C2 are connected in series the equivalent capacitance Ceq = (C1 * C2 ) / (C1+ C2) , which is even less than the smaller among C1 & C2 . Thus, from equation (1), it can be concluded that Voltage across the capactior will be less than V1 but more than V2 .

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