When resistors are placed in parallel, the voltage across one resistor is (more/less/the same) than the voltage of the battery and the current going through the battery is (more/less/the same) than the current through a simple circuit. Therefore, the overall resistance of a circuit where resistors are placed in parallel is (higher/lower/the same) than the overall resistance of a simple circuit.

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Describe uniform velocity and variable velocity in short

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