1). When air-filled, a particular parallel-plate capacitor has a capacitance of c1=18.2F. When the gap between the plates is filled with a dielectric oil, the capacitance changes to c2=31.4F. A potential difference of 12V is applied.

a). Input an expression for the electric permittivity of the oil.

b). What is the permittivity, in squared coulombs per newton per squared meter, of this oil (C^2/(Nm^2)?

c). How much additional charge, in coulombs, does the capacitor hold when filled with oil relative to when it's filled with air?

2). A capacitor of capacitance C = 3.5 F is initially uncharged. It is connected in series with a switch of negligible resistance, a resistor of resistance R = 8.5 k, and a battery which provides a potential difference of VB = 130 V.

a). Calculate the time constant for the circuit in seconds.

b). After a very long time after the switch has been closed, what is the voltage drop VC across the capacitor in terms of VB?

c). Calculate the charge Q on the capacitor a very long time after the switch has been closed in C.

d). Calculate the current I a very long time after the switch has been closed in A.

e). Calculate the time t after which the current through the resistor is one-third of its maximum value in s.

f). Calculate the charge Q on the capacitor when the current in the resistor equals one third its maximum value in C.

3). A heart defibrillator being used on a patient has an RC time constant of 8.5 ms due to the resistance of the patient's body and the capacitance of the defibrillator.

= 8.5 ms C = 5.5 F V = 13 kV

a). If the defibrillator has a 5.5 F capacitance, what is the resistance of the path through the patient in k? (You may neglect the capacitance of the patient's body and the resistance of the defibrillator.)

b). If the initial voltage is 13 kV, how long does it take to decline to 6.00 102 V in ms?