1 . A parallel-plate capacitor is made of two flat metal plates pressed against

Question

1. A parallel-plate capacitor is made of two flat metal plates pressed against a thin slab of dielectric material. The capacitor is connected to a power supply, and a potential difference of 70 V is applied to the plates. With the power supply disconnected, the dielectric material is removed and the potential difference between the plates is measured to be 575 V. What is the dielectric constant of the material that was initially used to fill the gap between the plates?   

2. A 2 ? resistor is mounted in parallel with a resistor R=5 ?, and this combination is connected in series with an 8 ? resistor and a 12 Volts battery. What is the current through the R resistor?   Amp

3. A charging RC circuit controls the intermittent windshield wipers in a car. The emf is 12.0 V. The wipers are triggered when the voltage across the 120

Explanation / Answer

1.

The dielectric constant is the ratio of the field without the dielectric (E0) to the net field (E) with the dielectric:

k = E0/E

Since E is always less than or equal to E0, the dielectric constant is greater than or equal to 1.

E0 = 575 and E = 70 so k = 575/70 = 8.214

So the dielectric constant is 8.214

2.I think it should be about 0.36A (possible rounding errors here), assuming I understand the question right.

OK, how I did it. Your circuit consists of 2ohm and 5ohm resistors in parallel, and a 8ohm resistor in series with this combination; 12V is across the resistor network. It should look something like this...

.........____ 5?__
....... |................|
0V__|.................|__8?__12V
........|____2?___|

And the 0V and 12V connect together through the battery.

Now, the resistance of the parallel section is 1/Rp = 1/R1+1/R2.... R1= 5ohm, R2=2ohm, so Rp=1.42ohm. Treat this as a voltage divider with the 8ohm; the voltage across the parallel section is Vp = Vt * Rp/(Rp+8) = 1.808V. Now, current I = V/R; V is 1.808V and R is 5ohms (I think this is the one you're looking for). I = 0.3616A.

3.Calculated 7115?. Possible practical resistor to use 7k1

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