A circuit contains four capacitors in parallel (10 F, 3 F, 7 F, and 1 F). What is the equivalent capacitance of this circuit?
1 answer:
The equivalent capacitance () of an electrical circuit containing four capacitors which are connected in parallel is equal to: A. 21 F.
Basically, the components of an electrical circuit can be connected or arranged in two forms and these are;
- Series circuit
- Parallel circuit
A parallel circuit can be defined as an electrical circuit with the same potential difference (voltage) across its terminals. This ultimately implies that, the equivalent capacitance () of two (2) capacitors which are connected in parallel is equal to the sum of the individual (each) capacitances.
Mathematically, the equivalent capacitance () of an electrical circuit containing four capacitors which are connected in parallel is given by this formula:
Ceq = C₁ + C₂ + C₃ + C₄
Substituting the given parameters into the formula, we have;
Ceq = 10 F + 3 F + 7 F + 1 F
Equivalent capacitance, Ceq = 21 F.
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A) The space time coordinate x of the collision in Earth's reference frame is
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B) The space time coordinate t of the collision in Earth's reference frame is
Explanation:
We are told a rocket travels in the x-direction at speed v=0,70 c (c=299792458 m/s is the exact value of the speed of light) with respect to the Earth. A collision between two comets is observed from the rocket and it is determined that the space time coordinates of the collision are (x',t') = (3.4 x 10¹⁰ m, 190 s).
An event indicates something that occurs at a given location in space and time, in this case the event is the collision between the two comets. We know the space time coordinates of the collision seen from the reference frame of the rocket and we want to find out the space time coordinates in Earth's reference frame.
<em>Lorentz transformation</em>
The Lorentz transformation relates things between two reference frames when one of them is moving with constant velocity with respect to the other. In this case the two reference frames are the Earth and the rocket that is moving with speed v=0,70 c in the x axis.
The Lorentz transformation is
prime coordinates are the ones from the rocket reference frame and unprimed variables are from the Earth's reference frame. Since we want position x and time t in the Earth's frame we need the inverse Lorentz transformation. This can be obtained by replacing v by -v and swapping primed an unprimed variables in the first set of equations
First we calculate the expression in the denominator
then we calculate t
finally we get that
then we calculate x
finally we get that
Answer:
Explanation:
Given that the airplane starts from the rest (this is initial velocity equals to zero) and accelerates at a constant rate, position can be described like this: where x is the position, t is the time a is the acceleration and
is initial velocity. In this way acceleration can be found.
.
Now we are able to found velocity at any time with the formula: