Il) Multiple Choice (2 pts/problem) If 500 J of work are required to carry a 40C
ID: 778026 • Letter: I
Question
Il) Multiple Choice (2 pts/problem) If 500 J of work are required to carry a 40C charge from one point to another, the potential difference between these two points is: if the electric field is in the positive x direction and has a magnitude given by E-Cx2 where C is a constant, then the electric potential may be given by: o 2Cx 0.32.5 V o 20,000V o 0.08 V CX epends on the path taken o None of the above The diagram below shows 4 pairs of large parallel conducting plates with same distance betweern them. The value of the electric potential is given for each plate. Rank the pairs according to the magnitude of the electric potential between them. Let Q denote charge, V denote potential difference and U denote stored energy. Of these quantities, capacitors connected in series must have the same Qonly o V only o Uonly 40 120 U and Q only Vand U only o 2,3,1,4 o 3,2,4,1 2,4,1,3 1,2,3,4 o 4,3,2,1 o ) The networks of identical resistors and capacitors below are all connected across identical ideal batteries. Rank each circuit in terms of the time it takes to charge each capacitor to 75% of its maximum charge, from greatest to least. Let I denote Current, V denote potential difference, and P denote power dissipated. Of these quantities, resistors connected in parallel must have 2. the same: o Ion o V only o P only o P nl T2 >T3 >T P and V onlyExplanation / Answer
(1) Expression for the work is -
W = Q*V
=> 500 = 40 * V
=> V = 500 / 40 = 12.5 V
(8) When the capacitors are in series, only the charge Q across each capacitors are same like when the resistors are in series, current across each are the same.
(11) Time constant , T = RC
so, time constant for (1) = 2RC
time constant for (2) = (R/2)C
time constant for (3) = RC
so charging time of (1) > charging time of (3) > charging time of (2)
(4) To find out the electric potential, integrate E with respect to x.
E = Cx^2
Integrate E = Cx^3 / 3
(5) Electric potential = V1 - V2
(1) V1-V2 = 70 - (-20) = 90 V
(2) V1 - V2 = 70-20 = 50 V
(3) V1-V2 = 90 - (-10) = 100 V
(4) V1 - V2 = 90 - 30 = 60 V
Now, rank it from lowest to the highest.
(12) Parllel means same potential difference means voltage.