Answer:
r₁/r₂ = 1/2 = 0.5
Explanation:
The resistance of a wire is given by the following formula:
R = ρL/A
where,
R = Resistance of wire
ρ = resistivity of the material of wire
L = Length of wire
A = Cross-sectional area of wire = πr²
r = radius of wire
Therefore,
R = ρL/πr²
<u>FOR WIRE A</u>:
R₁ = ρ₁L₁/πr₁² -------- equation 1
<u>FOR WIRE B</u>:
R₂ = ρ₂L₂/πr₂² -------- equation 2
It is given that resistance of wire A is four times greater than the resistance of wire B.
R₁ = 4 R₂
using values from equation 1 and equation 2:
ρ₁L₁/πr₁² = 4ρ₂L₂/πr₂²
since, the material and length of both wires are same.
ρ₁ = ρ₂ = ρ
L₁ = L₂ = L
Therefore,
ρL/πr₁² = 4ρL/πr₂²
1/r₁² = 4/r₂²
r₁²/r₂² = 1/4
taking square root on both sides:
<u>r₁/r₂ = 1/2 = 0.5</u>
Answer:
blue star is hotter than red
Explanation:
The colour of a star depends on its temperature.
Lesser the temperature means lesser be the energetic. less energy means longer wavelength. Between blue and red, red colour has longer wavelength. So, the red colored star is colder than blue coloured star.
Blue coloured star is hotter than red coloured star.
If 56.5kJ are needed to raise the temp by 90°C and if the heater is 60% efficient that means that:
60% X y = 56.5kJ
where y is the electrical energy in kJ that the heater will use.
y = 94.2kJ
Answer:
Explanation:
Given a parallel plate capacitor of
Area=A
Distance apart =d
Potential difference, =V
If the distance is reduce to d/2
What is p.d
We know that
Q=CV
Then,
V=Q/C
Then this shows that the voltage is inversely proportional to the capacitance
Therefore,
V∝1/C
So, VC=K
Now, the capacitance of a parallel plate capacitor is given as
C= εA/d
When the distance apart is d
Then,
C1=εA/d
When the distance is half d/2
C2= εA/(d/2)
C2= 2εA/d
Then, applying
VC=K
V1 is voltage of the full capacitor V1=V
V2 is the required voltage let say V'
Then,
V1C1=V2C2
V × εA/d=V' × 2εA/d
VεA/d = 2V'εA/d
Then the εA/d cancels on both sides and remains
V=2V'
Then, V'=V/2
The potential difference is half when the distance between the parallel plate capacitor was reduce to d/2
Answer:
The time taken to complete her run is 1.9 hr.
Explanation:
Speed is a scalar quantity and it is defined as the ratio of distance covered to the time taken to cover that distance. As distance is also a scalar quantity, so the directions given in the problem can be ignored. Thus, the distance covered by the jogger is the sum of kilometers given in problem.
Distance covered = 6+5+4 = 15 km
And the speed is given as 8 km/hr.
So the time taken will be ratio of distance to speed.
So the jogger will take 1.9 hr to complete her run.