Why does centripetal force point inwards? When I am turning a sharp curve in my car, I feel myself getting pushed outwards. So shouldn't centripetal force points outwards?
What you are feeling is the car door exerting an inward force on you. Centripetal force must point inwards because your change in velocity points inwards.
I have a capacitor in series with a resistor in a circuit powered by a 5V battery. What is the current running through the circuit?
There is zero current in this circuit because in a purely DC circuit, a capacitor essentially acts as an open wire, so no current will flow through the capacitor. This means that the voltage drop across the resistor is zero (V=IR and I=0) so then the voltage across the capacitor must be 5V in order to satisfy Kirchhoffs Loops Rule.
If protons are positively charged, how are they held together in the nucleus? wouldn't they repel each other away?
Protons are held together by a force known as the strong nuclear force, which is much greater in magnitude then the electromagnetic force that repels them away.