If the voltage across the first capacitor (the one with capacitance
1 answer:
The answer to this question is: it depends. It depends on the arrangement of the capacitors in a circuit: it can be either in series or in parallel. The difference is shown in the picture.
Capacitors are like batteries in a way that they store power from the source. It has some rules depending on the type of circuit. For parallel circuits, the voltage across each capacitor is equal. Therefore, V₁=V₂=V₃.
On the other hand, if the capacitors are arranged in series, the voltage across each capacitor should add up to the total voltage of the source. Therefore, V₁+V₂+V₃ = Total Voltage.
Capacitors are like batteries in a way that they store power from the source. It has some rules depending on the type of circuit. For parallel circuits, the voltage across each capacitor is equal. Therefore, V₁=V₂=V₃.
On the other hand, if the capacitors are arranged in series, the voltage across each capacitor should add up to the total voltage of the source. Therefore, V₁+V₂+V₃ = Total Voltage.
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Answer
a) Using dimensional analysis we cannot derive the relation, But we can check the correctness of the formula.
now, L H S
s = distance
dimension of distance = [M⁰L¹T⁰]
now, equation on the right hand side
R H S
u = speed
u = m/s
Dimension of speed = [M⁰L¹T⁻¹]
dimension of time
t = sec
Dimension of time = [M⁰L⁰T¹]
Dimension of 'ut' = [M⁰L¹T⁻¹][M⁰L⁰T¹]
= [M⁰L¹T⁰]
now, acceleration= a
a = m /s²
dimension of acceleration = [M⁰L¹T⁻²]
dimension of (at²) = [M⁰L¹T⁻²][M⁰L⁰T¹][M⁰L⁰T¹]
= [M⁰L¹T⁰]
hence, the dimension are balanced.
so, L H S = R H S
b) Moment of inertia of hollow sphere =
Moment of inertia of solid sphere =
we know,
Torque is the force that causes rotation
If the same amount of torque is applied to both spheres the sphere with bigger moment of inertia would have smaller angular velocity.
Thus the solid sphere would accelerate more.