Capacitance of a conductor is `1muF`. What charge is required to raise its potential to `100 V`?
Text Solution
AI Generated Solution
The correct Answer is:
To find the charge required to raise the potential of a conductor to a certain voltage, we can use the formula that relates capacitance (C), charge (Q), and voltage (V):
\[ Q = C \times V \]
### Step-by-Step Solution:
1. **Identify the given values:**
- Capacitance (C) = 1 microfarad (µF)
- Voltage (V) = 100 volts (V)
2. **Convert capacitance to standard units:**
- 1 microfarad (µF) = \( 1 \times 10^{-6} \) farads (F)
- Therefore, \( C = 1 \times 10^{-6} \, \text{F} \)
3. **Substitute the values into the formula:**
- Using the formula \( Q = C \times V \):
\[
Q = (1 \times 10^{-6} \, \text{F}) \times (100 \, \text{V})
\]
4. **Calculate the charge:**
\[
Q = 1 \times 10^{-6} \times 100 = 1 \times 10^{-4} \, \text{C}
\]
5. **Convert the charge to microcoulombs:**
- Since \( 1 \, \text{C} = 10^{6} \, \mu\text{C} \):
\[
Q = 1 \times 10^{-4} \, \text{C} = 100 \, \mu\text{C}
\]
### Final Answer:
The charge required to raise the potential of the conductor to 100 V is **100 microcoulombs (µC)**.
To find the charge required to raise the potential of a conductor to a certain voltage, we can use the formula that relates capacitance (C), charge (Q), and voltage (V):
\[ Q = C \times V \]
### Step-by-Step Solution:
1. **Identify the given values:**
- Capacitance (C) = 1 microfarad (µF)
...
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