The capacitors in each circuit are fully charged before the switch is closed. Rank, from longest to shortest, the length of time the bulbs (resistors) stay lit in each circuit.

The concept used in this is circuit analysis using the simplification of resistors and capacitors.

Explanation:

The time constant for each of the circuits in figure A, B, C, D and E. Therefore, rank the length of time the bulbs stay lit from longest to shortest by using the value of time constant for each circuit. The rank of the time constant of the circuit is C > A = E > B > DC  > A = E > B > D.

Capacitance is the central concept in electrostatics and constructed devices called capacitors are essential elements of electronic circuits.

If more charge is placed on the conductor the voltage increases proportionately. The ratio of the charge to the voltage is called the capacitance C of the conductor C= q/v.

The resistance increases if you add resistors in series and decreases if you add them in parallel. on the other hand the capacitors increases if it is added parallel and decreases if added in series. hence the circuit longest time constant takes longest time to discharge.

answer: the answer is a

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west