How will the current change if the voltage in a circuit is held constant while the resistance halves? 1. the current remains unchanged. 2. it's impossible to predict. 3. the current quadruples. 4. the current doubles. 5. the current halves?

Calculate the capacitance of a system that stores 2.0 x 10^-10c of charge at 100.0 v. use c=q/v. a. 2.0 x 10^-12 f b. 2.0 x 10^-8 f c. 5.0 x 10^11 f d. 5.0 x 10^7 f

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)

Aparticle's position is given by x = 3.00 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) what is its velocity at t = 1 s? (b) is it moving in the positive or negative direction of x just then? (c) what is its speed just then? (d) is the speed increasing or decreasing just then? (try answering the next two questions without further calculation.) (e) is there ever an instant when the velocity is zero? if so, give the time t; if not, answer "0". (f) is there a time after t = 3 s when the particle is moving in the negative direction of x? if so, give the time t; if not, answer "0".