Question
Question: A \(1\mu F\) and a \(2\mu F\) capacitor are connected in series across a \(1200\,{\rm{V}}\) supply. ...
A 1μF and a 2μF capacitor are connected in series across a 1200V supply. The charged capacitors are disconnected from the line and from each other and are now reconnected with the terminals of like sign together. Find the final charge on each capacitor and the voltage across each capacitor:
A. Charges on capacitors are 1400/3μC and 3200/3μC, and the potential difference across each capacitor is 1600/3V
B. Charges on capacitors are 1600/3μC and 3200/3μC, and the potential difference across each capacitor is 1600/3V
C. Charge on each capacitor is 1600μC and potential difference across each capacitor is 800V.
D. Charge and potential difference across each capacitor are zero
Solution
In this solution, find out the charge from those charged capacitors which are 1μF and a 2μF. Then, find out the voltage from each capacitor and put all the value to find the voltage across the capacitor.
Complete step by step solution:
We have,
Capacitor 1μF and a 2μF
Voltage, 1200V
Step 1:
1200−1q−2q=0\1200=1q+2q\1200=23q\q=32×1200\q=800μC
Hence, the charge on each capacitor is 800μC
Step 2: Finding V1 and V2
V1=C1q=1800=800V
V2=C2q=2800=400V
Step 3:
Here,
q1′+q2′=1600 …… (i)
So, 1q′1−2q′2=0
Or,
q2′=2q1′
From equation (i),
3q′1=1600q′1=31600μC\3q′2=33200μC
Hence,
V=C1+C2q1+q2 =31600V
So, the required answer is option B Charges on capacitors are 1600/3μC and 3200/3μC, and the potential difference across each capacitor is 1600/3V.
Additional information:
Capacitor: A capacitor is an electrical energy storage device in an electric field. It has two terminals and is a passive electronic component. Capacitance is the consequence of a condenser. Initially, the condenser was called a condenser or condensation. A capacitor is a passive electrical, two-terminal component used to store electrostatic energy in an electric field. A condenser is not dissipating energy, unlike a resistance. A condenser instead stores energy between its plates as an electrostatic field.
Terminals: A terminal is the end of a driver from a part, computer or network. Electrons flow from the negative terminal to the positive terminal from a galvanic cell, like an ordinary AA battery, while the normal current is the opposite. Terminals are pins in a connector that supplies electricity to protect the connections. Almost always made up of metal, some use other conductive materials (carbon, silicon, etc.).
Note: Since the capacitance is in micro, so the amount of charge will also be in micro-units.