Answer: A and B
Explanation:
took the test:) hope this helps
<span>1) The differential equation that models the RC circuit is :
(d/dt)V_capacitor </span>+ (V_capacitor/RC) = (V_source/<span>RC)</span>
<span>Where the time constant of the circuit is defined by the product of R*C
Time constant = T = R*C = (</span>30.5 ohms) * (89.9-mf) = 2.742 s
2) C<span>harge of the capacitor 1.57 time constants
1.57*(2.742) = 4.3048 s
The solution of the differential equation is
</span>V_capac (t) = (V_capac(0) - V_capac(∞<span>))e ^(-t /T) + </span>V_capac(∞)
Since the capacitor is initially uncharged V_capac(0) = 0
And the maximun Voltage the capacitor will have in this configuration is the voltage of the battery V_capac(∞) = 9V
This means,
V_capac (t) = (-9V)e ^(-t /T) + 9V
The charge in a capacitor is defined as Q = C*V
Where C is the capacitance and V is the Voltage across
V_capac (4.3048 s) = (-9V)e ^(-4.3048 s /T) + 9V
V_capac (4.3048 s) = (-9V)e ^(-4.3048 s /2.742 s) + 9V
V_capac (4.3048 s) = (-9V)e ^(-4.3048 s /2.742 s) + 9V = -1.87V +9V
V_capac (4.3048 s) = 7.1275 V
Q (4.3048 s) = 89.9mF*(7.1275V) = 0.6407 C
3) The charge after a very long time refers to the maximum charge the capacitor will hold in this circuit. This occurs when the voltage accross its terminals is equal to the voltage of the battery = 9V
Q (∞) = 89.9mF*(9V) = 0.8091 C
Answer:
Approximately 
to the right (assuming that both astronauts were originally stationary.)
Explanation:
If an object of mass 
is moving at a velocity of 
, the momentum 
of that object would be 
.
Since momentum of this system (of the astronauts) conserved:
.
Assuming that both astronauts were originally stationary. The total initial momentum of the two astronauts would be 
since the velocity of both astronauts was 
.
Therefore:
.
The final momentum of the first astronaut (
, 
to the left) would be 
to the left.
Let 
denote the momentum of the astronaut in question. The total final momentum of the two astronauts, combined, would be 
.
.
Hence, 
. In other words, the final momentum of the astronaut in question is the opposite of that of the first astronaut. Since momentum is a vector quantity, the momentum of the two astronauts magnitude (
) but opposite in direction (to the right versus to the left.)
Rearrange the equation to obtain an expression for velocity in terms of momentum and mass: 
.
.
Hence, the velocity of the astronaut in question (
) would be to the right.
<h2>
Option A is the correct answer.</h2>
Explanation:
A 10-ω resistor and a 30-ω resistor are connected in series across a 100-V battery
Total resistance = 10 + 30 = 40 ω
We have
Voltage = Current x resistance
100 = I x 40
I = 2.5 A
In series current in all the resistors are same, that is 2.5 A
Voltage in 10ω resistor, V = I x 10 = 2.5 x 10 = 25 V
In parallel connection potential in all the resistors are same.
Voltage in 10ω resistor, V = 100 V
The ratio of the potential difference across the 10-ω resistor in the series combination to that of the 10-ω resistance connected in parallel = 25/100 = 1/4
Option A is the correct answer.
