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.
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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