Electric current problems with answers

Flux through a Cube (Eigure 1) A cube has one corner at the origin and the opposite corner at the point (L, L, L). The sides of the cube are parallel to the coordinate planes

A slab of insulating material of uniform thickness d, lying between ${\displaystyle \frac{-d}{2}}$ to ${\displaystyle \frac{d}{2}}$ along the x axis, extends infinitely in the y and z directions, as shown in the figure. The slab has a uniform charge density ${\displaystyle \rho }$. The electric field is zero in the middle of the slab, at x=0. Which of the following statements is true of the electric field $E_{vec}$ at the surface of one side of the slab?

Answer the following T/F questions based on the behavior of the circuit in the above Figure 5:
(1) A transient current flows for a short time after the RELAY is switched to either the N.O.("normally open") or N.C. ("normally closed") position.
(2)The transient currents that flow in this experiment decays exponentially to zero.
(3)The capacitor charge Q exponentially decays to zero when the RELAY is thrown to position N.O.
(4)When the current I is positive, the capacitor charge Q is decreasing.
(5)When the current I is positive, the measured VOLTAGE IN 2 will be negative.
(6)When the capacitor charge Q is positive, the measured VOLTAGE IN 1 is positive.
(7)The quantity t1/2=? ln 2 is called the half-life of an exponential decay, where ?=RC is the time constant in an RC circuit. The current in a discharging RC circuit drops by half whenever t increases by ${\displaystyle t_{\frac{1}{2}}}$. For a circuit with R=2 k? and C=3 ?F, if the current is 6 am at t=5 ms, at what time (in ms) will the current be 3 mA?

A person who starting from rest at the top of a cliff swings down at the end of a rope,releases it, and falls into the water below. There are two paths bywhich the person can enter the water. Suppose he enters the waterat a speed of 13 m/s via path 1. How fast is he moving on path 2 when he releases the rope at a height of 5.20 m above the water? Ignore the effects of air resistance.

A 12-V battery is connected to terminals A and B in the above Figure.
(a) Given that R = 75 ohms, find the current in each resistor.
(b) Suppose the value of R is increased. For each resistor in turn, state whether the current flowing through it increases or decreases. Explain.

Two resistors, A and B, are connected in parallel across a 6.0V battery. The current through B is found to be 2.0 A. When the two resistos are connected in series to the 6.0 V battery,a voltmeter connected across the resistor A measures a voltage of4.0 V. Find the resistances of A and B.

(a) Determine the electric field E at the origin O in Figure due to the two charges at A and B. (Type your answer using k for proportionality constant, Q for charge and L for the length l.)
(b) Repeat, but let the charge at B be reversed in sign.

 
Consider the three circuits shown above. All the resistors and all the batteries are identical. Which of the statements are true and which ones are false? 
1)The power dissipated in circuit A is twice the power dissipated in circuit B. 
2) The current through a resistor is the same in circuits A and C. 
3) The current through a resistor is the same in circuits A and B. 
4) The voltage across a single resistor in circuit C is twice the voltage across a single resistor in circuit B. 
5) The total power dissipated in circuit C is twice the total power dissipated in circuit B.