Problem 13 (8 points) Suppose y across the itage ill equal that of the battery (

Question

Problem 13 (8 points) Suppose y across the itage ill equal that of the battery (9V). Next, suppose you carefully imset a dielectric inulatsor between de planes Vks dh The ou connect a battery to an air-illed parallel plate capacitos Vilke dhat shncrwn in Vve 2o pyou then disks oft tve pluse, ti tery voltage is 9V and the capacitance is 200 pF. You then disconnnect tihe basttery wnd wenure t wola een terminals like that shown in Figure 6 (b) below. Assuming no charge leaks oft te plane, tisreá shown in Figure 6 (c) below (without discharging the capacitor in any way). Te dielectr'ic wsilator ls te enire ue between the plates. The relative dielectric constant of the insulator is rAA.What is the new mewared volkage wcrons d open terminals? (Hint: it will be less than Va Area A Area A men dielectric Disconnect Vat Meanuted voltag wth dvlectrc Measured voltage = Vbat Vbat Figure 6 Parallel plate capacitor under different conditions

Explanation / Answer

Initially, when the air is the medium between the parallel plates we have the voltage of 9 volt across the capacitor.

Now we are removing the battery of 9 volts so the capacitor must have stored some charge, which is given by the formula

Q = C * V

here Q = charge

C = capacitance

V = voltage across capacitor

Hence Q = (200 pF) * (9 Volt) = 1800 pCoulomb

Now since there is no leakage of charge even after the addition of dielectric material so charge Q is fixed.

Now the new capacitance will be C = 200pF * 4.4 = 880 pF

Now using the same formula as above to find the voltage across the capacitor,

V = Q / C = 1800 pC / 880 pF = 2.045 Volt

Hence solved.

Please see that the obtained result is less than previous one as given in hint!

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