Question

you are given 2 capacitor of 2uf and 3uf what are the maximum and minimum values of capacitance that can be obtained by combining them​

Answer 1

Answer:

Minimum value =1.2uf

Maximum value =5uf

Explanation:

Given capacitance values are2uf and 3uf

Minimum value of capacitance can be obtained in series combination

1/C = 1/2 + 1/3 = 0.833

C =1/0.833 = 1.2uf

Maximum value of capacitance can be obtained in parallel combination

C =2+3 =5 uf

Answer 2

Given:

Capacitors of $2$μ$F$ and $3$μ$F$

To find:

The value of maximum and minimum capacitance.

Solution:

We know, according to the definition, Potential difference across a conductor is directly proportional to the charge stored in the conductor.

                      $Q$ ∝ $V$

                      $Q=kV$

                      $Q=CV$

C is called as the capacitance of the capacitor.

We can clearly see that, $C$ ∝ $\frac{1}{V}$ .

Hence, for minimum capacitance in the capacitor, the potential difference required should be more in the circuit and vice versa.

As we know, in series combination, the potential difference in the circuit gets add up thus, potential difference increases and hence the capacitance

decreases.

                        $\frac{1}{C_{eq} }= \frac{1}{C_{1} }+ \frac{1}{C_{2} }$

Similarly, in parallel combination of the capacitors, the potential difference decreases hence the capacitance increases.

                       $C_{eq}= C_{1}+ C_{2}$

Solution:

We have,  $C_{1}=2$ μ$F$    ;  $C_{2}=3$ μ$F$

Step 1

For maximum capacitance,

$C_{eq}= C_{1}+ C_{2}$

$C_{eq}= 2+3$

$C_{eq}=$ $5$ μ$F$

Step 2

For minimum capacitance,

$\frac{1}{C_{eq} }= \frac{1}{C_{1} }+ \frac{1}{C_{2} }$

$\frac{1}{C_{eq} }= \frac{1}{2 }+ \frac{1}{3 }$

$\frac{1}{C_{eq} }= \frac{5}{6 }$

${C_{eq} }= \frac{6}{5 }$

${C_{eq} }= 1.2$ μ$F$

Final answer:

Hence,

1. The maximum value of capacitance will be obtained on the connecting the capacitors in parallel that is 5μF.
2. The minimum vale of capacitance will be obtained on connecting the capacitors in series that is 1.2μF.