Relation between induction voltage, condenser and resistance

In summary, the relation between induction voltage, condenser, and resistance follows Ohm's law, where the voltage (V) is equal to the product of the current (I) and resistance (R). The presence of a condenser in a circuit can impact the induction voltage by storing and releasing electric charge. Resistance plays a crucial role in the circuit by determining the current flow and can affect the behavior of the condenser. The value of the condenser can also impact the induction voltage by affecting the charge storage. Finally, all three components can be manipulated to achieve a desired outcome in a circuit.
  • #1
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Homework Statement


Check out the attached image.
The electromagnetic field B is constant.
The rod is moving through the rail and an inductive emf V is produced on the closed loop.
Due to that, the condenser C has a voltage difference Vc.
Question:
Express the relation between the total emf produced V and the condenser's voltage difference Vc in function of C and the resistance r (check out the attached image).

Homework Equations




The Attempt at a Solution


Well, no idea at all.
I tried this:
The total emf produced V = Vc + voltage of the resistance Vr
As the condenser and the resistor are connected by conductors, they must have the same voltage, so Vc = Vr
Then, I will get V= 2Vc.
BUT, the question asks me to express the relation between V and Vc in function of C and r. What I got is a simple V=2Vc.

Please help.
 

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  • #2


Hello there,

Thank you for bringing this question to my attention. It seems like you have the right idea, but the equation you have written is not quite complete. Let me explain further.

First, let's define the symbols we are working with:
V = total emf produced
Vc = voltage difference of the condenser
Vr = voltage difference of the resistor
r = resistance of the resistor
C = capacitance of the condenser

Now, as you correctly stated, because the condenser and resistor are connected by conductors, they must have the same voltage. Therefore, we can write the equation Vc = Vr.

Next, we know that the total emf produced is equal to the sum of the emf produced by the condenser and the emf produced by the resistor. In other words, V = Vc + Vr.

Now, we can substitute Vr with Vc in the equation above, since we know that they are equal. This gives us V = Vc + Vc, or simply V = 2Vc.

However, this is not the complete answer. We need to express V in terms of C and r. To do this, we need to use the equation for the voltage difference of a capacitor, which is Vc = Q/C, where Q is the charge on the capacitor and C is the capacitance.

We also know that the current flowing through the resistor is equal to the current flowing through the capacitor, since they are connected in series. Therefore, we can use Ohm's law to write Vr = I*r, where I is the current flowing through the circuit.

Now, we can substitute these equations into our original equation for V, which gives us:
V = Vc + Vr
V = Q/C + I*r

But we know that Q = CVc, so we can rewrite this as:
V = CVc/C + I*r
V = Vc + I*r

And finally, we can substitute Vc = Vr into this equation, which gives us:
V = Vr + I*r
V = Vc + I*r

And there you have it! The relation between the total emf produced V and the condenser's voltage difference Vc in terms of C and r is V = Vc + I*r.

I hope this helps. Let me know if you have any further questions or need any clarification.[
 

Related to Relation between induction voltage, condenser and resistance

1. What is the relation between induction voltage, condenser, and resistance?

The relation between induction voltage, condenser, and resistance follows Ohm's law, which states that the voltage (V) across a circuit is equal to the product of the current (I) and the resistance (R). In this case, the induction voltage is caused by the changing magnetic field in the circuit, and the condenser and resistance both affect the current flowing through the circuit.

2. How does the presence of a condenser affect the induction voltage?

The presence of a condenser in a circuit can impact the induction voltage by storing electric charge and releasing it back into the circuit when the voltage changes. This can cause fluctuations in the induction voltage and can also affect the rate at which the magnetic field changes.

3. What role does resistance play in the relation between induction voltage and condenser?

Resistance plays a crucial role in the circuit as it determines the amount of current flowing through the circuit. A higher resistance can reduce the flow of current, which in turn can affect the induction voltage and the behavior of the condenser in the circuit.

4. How does the value of the condenser impact the induction voltage in a circuit?

The value of the condenser, also known as capacitance, can impact the induction voltage in a circuit by affecting the amount of charge it can store and release. A higher capacitance can lead to a larger charge storage, resulting in a higher induction voltage, while a lower capacitance can lead to a smaller charge storage and a lower induction voltage.

5. Can the induction voltage, condenser, and resistance be manipulated to achieve a desired outcome in a circuit?

Yes, the induction voltage, condenser, and resistance can be manipulated to achieve a desired outcome in a circuit. By adjusting the values of these components, one can control the flow of current and the resulting induction voltage in the circuit. This can be useful in various applications, such as in electronic devices or power systems.

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