Please answer all with steps :(((

4. (a) (b) (C) 5. (a) (b) (C) 6. Electric current in a simple direct-current circuit In the following direct-current circuit, Find the magnitude and direction of the current through the circuit; Find the potential difference Vad = Va V4. Find the terminal voltage across the 3V battery Vac = Va VC. Resistor network and power dissipation: In the following circuit, Find the equivalent resistance between a and b; Find the power dissipated in the 21S) resistor; Find the power dissipated in the 69 resistor. Parallel-plate capacitor with a slab of dielectric inside A parallel-plate capacitor with air between the plates is connected to a 45 V battery. The capacitor is then disconnected from the battery without losing any of the charges on the plates. When a dielectric slab is inserted, completely lling the space between the plates, the potential difference between the plates drops to 11.25 V. What is the dielectric constant of the inserted material? If the dielectric slab is pulled partway out so it only lls 1/2 of the space between the plates, what is the potential difference between the plates? If the dielectric slab is free to slide in and out of the space between the plates, is an external force needed to move the dielectric slab from being completely lling the space between the plates (and at rest) to being only 50% lling the space between the plates ? (Hint: compare the change in energy stored in the capacitor and argue from there)