Question

Two capacitors C₁ = 5.2 μF ± 0.1 μF and c₂ = 12.2 μF are joined (i) In series (ii) In parallel. Find the net capacitance in these two cases.

• A. 2.8%, 1.23%
• B. 3.6%, 1.31%
• C. 3.4%, 1.3%
• D. 3.9%, 1.15%

Answer 1

Answer: (D)

3.9%, 1.15%

Answer 2

In parallel c = c₁ + c₂ and

$\frac{\Delta c}{c} \times 100 = \frac{\Delta c_{1} + \Delta c_{2}}{c_{1} + c_{2}} \times 100 = \frac{0.2x100}{17.4}$In series c =

$\frac{c_{1}c_{2}}{c_{1} + c_{2}}$

$\frac{\Delta c}{c} \times 100 = \left( \frac{\Delta c_{1}}{c_{1}} + \frac{\Delta c_{2}}{c_{2}} + \frac{\Delta c_{1} + \Delta c_{2}}{c_{1} + c_{2}} \right)100$

= $\left( \frac{0.1}{5.2} + \frac{0.1}{12.2} \right) \times 100 + 1.15 = 3.9\%$