What is the voltage across the capacitor plates

AI Thread Summary
A 15uF capacitor charged to 55V has its battery removed and a dielectric with a constant of 4.8 is inserted. The voltage across the capacitor plates after inserting the dielectric is calculated using the formula V = Vo/k, resulting in 11.5V. The discussion confirms that the capacitance value is irrelevant since charge (Q) remains constant, and an increase in capacitance leads to a decrease in voltage. Participants clarify that the voltage does indeed decrease by the factor of the dielectric constant. The final consensus is that the initial calculation of 11.5V is correct.
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Am I overthinking this problem?

A 15uF capacitor is connected ot a 55V battery and becomes fully charged. The battery is removed and the circuit is left open. A slab of dielectric material is inserted to completely fill the space between the plates. It has a dielectric constant of 4.8. What is the voltage across the capacitor plates after the slab is in place?

I'm thinking that I just use V = Vo/k = 55/4.8 =11.5V

This seems too easy and doesn't use the value for the capacitor.

Can anyone tell me if I'm totally off in my thinking?
 
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Other way around.

The introduction of a dieletric increases the capacitor's capacitance by a factor of k.

Q = CV and Q remains constant. As a result, if C increases by a factor of k, V must decrease by a factor of k.

You are correct that the actual value of the capacitance is irrelevant, as it cancels out.

- Warren
 
Sorry I'm confused, you said "Other way around" but based on what you wrote I have it correct that the voltage decreases by k, ie V = Vo/k
 
Woops, sorry, I read your response incorrectly and thought you had increased the voltage across the capacitor. Your answer is correct.

- Warren
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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