POSSIBLE POINTS: 100 Calculate the total resistance, total current, and current for each branch for a circuit with two light bulbs in parallel, one with 4 ohms and the other with
2.5 ohms. The battery is a 3.5 V battery

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

Given the position vector of the particle r(t)=(t+1)i+(t^2−1)j+2t k, find the particle's velocity and acceleration vectors at t=1

The charge on a charged sphere is: a)concentrated at its centerb)distributed uniformly throughout its volumec)clustered on its centerd)distributed uniformly over its surface