1. your are given the circuit below which contains four resistors r1 = 1.0 . , r2 = 4.0 . , r3 = 4.0 . , r4 = 5.0 . , and one capacitor c1 = 2.0 µf. (a) what is the current through the resistor r4? (b) what is the potential difference across the capacitor? (c) what is the charge on the capacitor? (d) what is the power dissipated by resistor r4?

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants