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Calculate the equivalent capacitance of capacitors C1=0.1 ext uF, C2=0.2 ext uF, C3=0.3 ext uF when connected in series and in parallel.

Physics

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here's the solution for .8:

Given capacitor values:
C1=0.1μFC_1 = 0.1 \mu\text{F}
C2=0.2μFC_2 = 0.2 \mu\text{F}
C3=0.3μFC_3 = 0.3 \mu\text{F}

Part i· 4 steps

in series

  1. Use the formula for the equivalent capacitance of capacitors connected in series.

    1Ceq=1C1+1C2+1C3\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}
  2. Substitute the given values into the formula.

    1Ceq=10.1μF+10.2μF+10.3μF\frac{1}{C_{eq}} = \frac{1}{0.1 \mu\text{F}} + \frac{1}{0.2 \mu\text{F}} + \frac{1}{0.3 \mu\text{F}}
  3. Calculate the sum of the reciprocals.

    1Ceq=10 (\muF)−1+5 (\muF)−1+3.333... (\muF)−1\frac{1}{C_{eq}} = 10 \text{ (\mu F)}^{-1} + 5 \text{ (\mu F)}^{-1} + 3.333... \text{ (\mu F)}^{-1} 1Ceq=18.333... (\muF)−1\frac{1}{C_{eq}} = 18.333... \text{ (\mu F)}^{-1}
  4. Find the equivalent capacitance by taking the reciprocal.

    Ceq=118.333...μFC_{eq} = \frac{1}{18.333...} \mu\text{F} Ceq≈0.0545μFC_{eq} \approx 0.0545 \mu\text{F}

    The equivalent capacitance in series is 0.0545 \muF\boxed{\text{0.0545 \mu F}}.

Part ii· 3 steps

in parallel

  1. Use the formula for the equivalent capacitance of capacitors connected in parallel.

    Ceq=C1+C2+C3C_{eq} = C_1 + C_2 + C_3
  2. Substitute the given values into the formula.

    Ceq=0.1μF+0.2μF+0.3μFC_{eq} = 0.1 \mu\text{F} + 0.2 \mu\text{F} + 0.3 \mu\text{F}
  3. Calculate the sum.

    Ceq=0.6μFC_{eq} = 0.6 \mu\text{F}

    The equivalent capacitance in parallel is 0.6 \muF\boxed{\text{0.6 \mu F}}.

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