A) State one application of a capacitor. b) The figure shows four capacitors connected to a battery of 12 volts Calculate: i) Effective capacitance. ii) Charge on 3.2µF. iii) P.d across 5µF

$$C_p = C_1 + C_2$$ $$C_p = 2 \, \mu\text{F} + 8 \, \mu\text{F}$$ $$C_p = 10 \, \mu\text{F}$$

$$\frac{1}{C_{eff}} = \frac{1}{C_a} + \frac{1}{C_p} + \frac{1}{C_b}$$ $$\frac{1}{C_{eff}} = \frac{1}{5 \, \mu\text{F}} + \frac{1}{10 \, \mu\text{F}} + \frac{1}{3.2 \, \mu\text{F}}$$ $$\frac{1}{C_{eff}} = \frac{1}{5} + \frac{1}{10} + \frac{10}{32}$$ $$\frac{1}{C_{eff}} = \frac{16}{80} + \frac{8}{80} + \frac{25}{80}$$ $$\frac{1}{C_{eff}} = \frac{16 + 8 + 25}{80}$$ $$\frac{1}{C_{eff}} = \frac{49}{80}$$ $$C_{eff} = \frac{80}{49} \, \mu\text{F}$$ $$C_{eff} \approx 1.63 \, \mu\text{F}$$

Uwezo jumla ni $\boxed{\text{1.63 } \mu\text{F}}$.

Katika mzunguko wa mfululizo, chaji jumla ni sawa na chaji kwenye kila capacitor.

$$Q_{total} = C_{eff} \times V_{total}$$ $$Q_{total} = \frac{80}{49} \, \mu\text{F} \times 12 \, \text{V}$$ $$Q_{total} = \frac{960}{49} \, \mu\text{C}$$ $$Q_{total} \approx 19.59 \, \mu\text{C}$$

$$Q_{3.2\mu\text{F}} = Q_{total}$$ $$Q_{3.2\mu\text{F}} \approx 19.59 \, \mu\text{C}$$

Chaji kwenye 3.2 µF ni $\boxed{\text{19.59 } \mu\text{C}}$.

Chaji kwenye 5 µF ni $Q_{total}$.

$$V_{5\mu\text{F}} = \frac{Q_{total}}{C_{5\mu\text{F}}}$$ $$V_{5\mu\text{F}} = \frac{\frac{960}{49} \, \mu\text{C}}{5 \, \mu\text{F}}$$ $$V_{5\mu\text{F}} = \frac{960}{49 \times 5} \, \text{V}$$ $$V_{5\mu\text{F}} = \frac{960}{245} \, \text{V}$$ $$V_{5\mu\text{F}} = \frac{192}{49} \, \text{V}$$ $$V_{5\mu\text{F}} \approx 3.92 \, \text{V}$$

Tofauti ya uwezo kwenye 5 µF ni $\boxed{\text{3.92 V}}$.