MHB Voltage Across 10, 20uF Capacitors in RC Circuit

AI Thread Summary
Two capacitors, 10 and 20 microfarads, connected in series and charged with a 100-volt battery, are analyzed for voltage across them after being discharged through a 2500-ohm resistor. The relevant formulas discussed include the relationship between voltage, capacity, and charge, as well as the discharge equation V_C = V_0 e^(-t/RC). The combined capacity of the capacitors in series is calculated using the formula 1/(1/C1 + 1/C2). It is confirmed that the voltage decays exponentially over time, not increases, with the decay characterized by the RC time constant. The discussion emphasizes the importance of correctly applying the negative sign in the discharge formula to reflect the expected behavior of the circuit.
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Two capacitors of value 10, 20 microfarads are
connected in series. Then charged with a 100 volt battery. If the capacitors is
disconnected from the battery, and then connected to a 2500
ohm resistor, what is the voltage across the capacitors after 1 second?
 
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LLand314 said:
Two capacitors of value 10, 20 microfarads are
connected in series. Then charged with a 100 volt battery. If the capacitors is
disconnected from the battery, and then connected to a 2500
ohm resistor, what is the voltage across the capacitors after 1 second?

Hi LLand314!

Can you come up with a couple of formulas that are applicable?

One for the relationship between voltage, capacity, and charge?
Another one for the discharge of a charged capacitor versus time?
And perhaps one for the combined capacity of 2 capacitors in series? (Wondering)
 
I like Serena said:
Hi LLand314!

Can you come up with a couple of formulas that are applicable?

One for the relationship between voltage, capacity, and charge?
Another one for the discharge of a charged capacitor versus time?
And perhaps one for the combined capacity of 2 capacitors in series? (Wondering)

these formulas?
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LLand314 said:
these formulas?

Yep.

When the capacitors get charged, a charge Q flows from the first to the second.
Afterwards, they both hold the same charge Q.

From your formulas, you can get that:
$$Q=C_1 V_1$$
$$Q=C_2 V_2$$
$$V_{total} = V_1 + V_2$$

What will the charge Q and the voltages be?
 
I like Serena said:
Yep.

When the capacitors get charged, a charge Q flows from the first to the second.
Afterwards, they both hold the same charge Q.

From your formulas, you can get that:
$$Q=C_1 V_1$$
$$Q=C_2 V_2$$
$$V_{total} = V_1 + V_2$$

What will the charge Q and the voltages be?

since the capacitors are in series can I just replace the 3 with a single using (1/(1/c1)+(1/c2))?
 
LLand314 said:
since the capacitors are in series can I just replace the 3 with a single using (1/(1/c1)+(1/c2))?

Yep, you can.
Since you didn't give a formula for the combined capacity of 2 capacitors in series, I assumed you didn't have that formula and had to do without.

Then the only thing left is to apply $V_C=V_0 e^{-t/RC}$.
 
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I like Serena said:
Yep, you can.
Since you didn't give a formula for the combined capacity of 2 capacitors in series, I assumed you didn't have that formula and had to do without.

Then the only thing left is to apply $V_C=V_0 e^{t/RC}$.
then 100e^(1/(2500*(6.666*10^-6)))?
 
LLand314 said:
then 100e^(1/(2500*(6.666*10^-6)))?

Yup! (Happy)
 
I like Serena said:
Yup! (Happy)

the voltage I get is a huge number how can it be so big?

edit: oh wait shouldn't it be Vc=V0e^(-t/rc)? a negative sign in the t/rc
 
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  • #10
LLand314 said:
the voltage I get is a huge number how can it be so big?

edit: oh wait shouldn't it be Vc=V0e^(-t/rc)? a negative sign in the t/rc

Quite right!

(Hmm. That minus sign also seems to be missing in your picture. (Worried))
 
  • #11
I like Serena said:
Quite right!

(Hmm. That minus sign also seems to be missing in your picture. (Worried))

Yes I see that, strange.
anyhow so my voltage should be small correct?
 
  • #12
LLand314 said:
Yes I see that, strange.
anyhow so my voltage should be small correct?

Correct.
The voltage really decays exponentionally instead of increasing.
And it decays with a characteristic time that is also called the RC-time.
 
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