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Romashka [77]
3 years ago
10

The current through each resistor in the two-resistor circuit is _________ the current through the resistor in the one-resistor

circuit (the circuit in Part A). The voltage across each resistor in the two-resistor circuit is ___________ the voltage across the resistor in the one-resistor circuit.
Physics
1 answer:
poizon [28]3 years ago
7 0

Answer:

Serial circuit.   the current is constant.  

            the voltage across a given resistor is half the rating in a one-resistor circuit.

Parallel circuit    the voltage is constant

the current is half the value of the current with a single resistor

Explanation:

To answer exactly this exercise, you need the diagram or the indication of the type of circuit being used, since there are two possibilities, let's consider the results of each one.

Serial circuit.

The two resistance are one after the other.

In this case the current in the resistor sides is the same, that is, the current is constant in the circuit.

The voltage is proportional to the value of each resistor and if the two resistors are equal, the voltage across a given resistor is half the rating in a one-resistor circuit.

Parallel circuit

the two resistance is next to each other.

In this case the voltage is constant, that is, the voltage across the two resistors is the same as in the case of a single resistor.

The current is inversely proportional to the value of the resistance

          i₁ = V / R₁

          i₂ = V / R₂

     

for a single resistance

           I = V / R

these currents are related

          i = i₁ + i₂

if the two resistors have the same value the current is half the value of the current with a single resistor

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part (a) v = 1.7 m/s towards right direction

part (b) Not an elastic collision

part (c) F = -228.6 N towards left.

Explanation:

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  • Mass of the first puck = m_1\ =\ 5\ kg
  • Mass of the second puck = m_2\ =\ 3\ kg
  • initial velocity of the first puck = u_1\ =\ 3\ m/s.
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Part (a)

Pucks are stick together after the collision, therefore the final velocities of the pucks are same as v.

From the conservation of linear momentum,

m_1u_1\ +\ m_2u_2\ =\ (m_1\ +\ m_2)v\\\Rightarrow v\ =\ \dfrac{m_1u_1\ +\ m_2u_2}{m_1\ +\ m_2}\\\Rightarrow v\ =\ \dfrac{5\times 3\ -\ 1.5\times 1.5}{5\ +\ 1.5}\\\Rightarrow v\ =\ 1.7\ m/s.

Direction of the velocity is towards right due to positive velocity.

part (b)

Given,

Final velocity of the second puck = v_2\ =\ 2.31\ m/s.

Let v_1 be the final velocity of first puck after the collision.

From the conservation of linear momentum,

m_1u_1\ +\ m_2u_2\ +\ m_1v_1\ +\ m_2v_2\\\Rightarrow v_1\ =\ \dfrac{m_1u_1\ +\ m_2u_2\ -\ m_2v_2}{m_1}\\\Rightarrow v_1\ =\ \dfrac{5\times 3\ -\ 1.5\times 1.5\ -\ 1.5\times 2.31}{5}\\\Rightarrow v_1\ =\ 1.857\ m/s.

For elastic collision, the coefficient of restitution should be 1.

From the equation of the restitution,

v_1\ -\ v_2\ =\ e(u_2\ -\ u_1)\\\Rightarrow e\ =\ \dfrac{v_1\ -\ v_2}{u_2\ -\ u_1}\\\Rightarrow e\ =\ \dfrac{1.857\ -\ 2.31}{-1.5\ -\ 3}\\\Rightarrow e\ =\ 0.1\\

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Given,

Time of impact = t = 25\times 10^{-3}\ sec

we know that the impulse on an object due to a force is equal to the change in momentum of the object due to the collision,

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