Help with Homework: Part a) Proven, Part b) Checked, Part c?) Stumped

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The discussion focuses on a homework problem involving a series circuit with a capacitor. Part a) has been proven, but part b) is questioned for its correctness, with suggestions to use the equation V_R = ε - V_C for clarity. The user is stumped on part c), where the current is stated to be constant, and the relationship i = dq/dt is mentioned. Several misunderstandings are highlighted, including the misuse of symbols for charge and incorrect calculations for current. The conversation emphasizes the importance of understanding the equations and their applications in circuit analysis.
Jozefina Gramatikova
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Homework Statement


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Homework Equations


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The Attempt at a Solution


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I proved part a)
Can you please check if part b) is correct?
I don't know what to do in part c)
 

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For part (c), the current is the same everywhere in a series circuit, and can be computed by ## i=\frac{dq}{dt} ## when there is a capacitor in the circuit, where ##q ## is the charge on the capacitor. This can also be used for part b. (Your part (b) is incorrect). Alternatively, you could compute ## V_R=\mathcal{E}-V_C ## where ## V_c=\frac{q}{C} ##.
 
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I get the feeling that you are trying to use some equations without fully understanding them.
1. Why do you think the equation I = q/t is right?
2. I do not see your attempt at part (a). That part is crucial to the understanding of the problem.
3. I do not understand your first value for q, which looks like q = 1 10^(-6) . 10
4. Then there is a second value for q = 3.93 10^(-6) C. Why did you use the same symbol for two different values?
5. The way you got the value for I = 0.08 A is wrong. That equation for I is not valid.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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