Four capacitors having capacitances of 2 µF, 6 µF, 14 µF and 5 µF are connected in parallel and this combination is across an ideal voltage source. If the charge on the 6 µF capacitor is 180 µC, what is the total charge on this circuit?
Four capacitors having capacitances of 2 µF, 6 µF, 14 µF and 5 µF are connected in parallel and this combination is across an ideal voltage source. If the charge on the 6 µF capacitor is 180 µC, what is the total charge on this circuit?
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![**Question:**
Four capacitors having capacitances of 2 µF, 6 µF, 14 µF, and 5 µF are connected in parallel and this combination is across an ideal voltage source. If the charge on the 6 µF capacitor is 180 µC, what is the total charge on this circuit?
- ○ 720 µC
- ○ 120 µC
- ○ 810 µC
- ○ 4860 µC
- ○ 1080 µC
- ○ 180 µC
**Explanation:**
Capacitors in parallel share the same voltage, \( V \). The charge on any capacitor in parallel is given by \( Q = C \times V \). Here, the charge \( Q \) on the 6 µF capacitor is 180 µC, so:
\[ V = \frac{Q}{C} = \frac{180 \, \mu C}{6 \, \mu F} = 30\, \text{V} \]
The total charge for capacitors in parallel is the sum of individual charges:
\[ Q_{\text{total}} = (2 + 6 + 14 + 5) \, \mu F \times 30 \, \text{V} \]
\[ = 27 \, \mu F \times 30 \, \text{V} \]
\[ = 810 \, \mu C \]
Therefore, the total charge on the circuit is 810 µC.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8daeabfb-08fc-4e08-b5f3-009f3913f10d%2F23d56c23-6900-4618-9fa9-c1716f20e209%2Fb5r47t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Four capacitors having capacitances of 2 µF, 6 µF, 14 µF, and 5 µF are connected in parallel and this combination is across an ideal voltage source. If the charge on the 6 µF capacitor is 180 µC, what is the total charge on this circuit?
- ○ 720 µC
- ○ 120 µC
- ○ 810 µC
- ○ 4860 µC
- ○ 1080 µC
- ○ 180 µC
**Explanation:**
Capacitors in parallel share the same voltage, \( V \). The charge on any capacitor in parallel is given by \( Q = C \times V \). Here, the charge \( Q \) on the 6 µF capacitor is 180 µC, so:
\[ V = \frac{Q}{C} = \frac{180 \, \mu C}{6 \, \mu F} = 30\, \text{V} \]
The total charge for capacitors in parallel is the sum of individual charges:
\[ Q_{\text{total}} = (2 + 6 + 14 + 5) \, \mu F \times 30 \, \text{V} \]
\[ = 27 \, \mu F \times 30 \, \text{V} \]
\[ = 810 \, \mu C \]
Therefore, the total charge on the circuit is 810 µC.
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