consider a circuit 7v, R1 1ohm, R2 3ohm, R3 2ohm, R4 1ohm, R5 2 ohm and current 7A Calculate the voltage across 1ohm resistor using 1- mesh analysis, 2-nodal analysis, 3-superposition, 4-thevenin's theorem, 5-Norton's theorem

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