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**Phys 180L 3: CAPACITANCE IN SERIES AND IN PARALLEL**

** **

**OBJECTIVE:**

The objective of this experiment is to study combinations of capacitors in series and in parallel.

**THEORY:**

If two conducting plates separated by a distance D and in parallel with each other is placed across a source of potential difference such as a battery or a power supply each plate becomes equally but oppositely charged up. This parallel arrangement of charged plates is called a capacitor. The magnitude of the charge on each plate is proportional to the potential difference placed across the capacitor, thus

Q ∝ V

Or

Q = CV,

Where C is the constant of proportionality or capacitance of the capacitor. The capacitance C can be defined as the ratio of the amount of charge on each plate per potential difference across the plates. The unit of capacitance is the Coulomb/Volt or Farad.

__Capacitors In Series:__

When capacitors are connected in series with each other, the amount of charge Q flowing through them is constant. They are placed directly across a battery of potential difference V, where V varies for each capacitor.

**V=V _{1}+V_{2}+V_{3} **

** **

**Q/C=(Q/C _{1}) +(Q/C_{2})+(Q/C_{3})**

** **

**Q=Q _{1}=Q_{2}=Q_{3}**

** **

**1/C _{eq}=(1/C_{1}) +(1/C_{2})+(1/C_{3}) **

** **

__ __

__Capacitors In Parallel:__

When capacitors are connected in parallel with each other, the amount of charge flowing through each capacitor is different. The voltage (V) passing through each capacitor is constant irrespective of the magnitude of the capacitor and the parallel combination of the number of capacitors.

**Q=Q _{1} + Q_{2 }+ Q_{3} **

** **

**C _{eq}V=C_{1}V_{1}+C_{2}V_{2}+C_{3}V_{3}**

_{ }

**V=V _{1}=V_{2}=V_{3} **

_{ }

**C _{eq}=C_{1}+C_{2}+C_{3}**

** **

**Procedure:**

For Series-

- A)
__Connecting capacitors in series:__

(i) Three capacitors are taken, C_{1} = 470 C_{2} = and C_{3} = 220. Connect the

capacitors in order as C_{1}, C_{2} and then C_{3} in the series circuit. Adjust the power supply to

supply 3 VDC by using a voltmeter.

(ii) Set the electrometer to read DC volts measuring V_{1}, V_{2} and V_{3} for each corresponding

capacitor. The values are recorded in the table.

(iii) Discharge each capacitor by touching the terminals wires of the capacitor to a metal before changing the voltage.

(iv) Repeat step 2 and 3 for power supply voltages of 5 VDC and 10 VDC.

- B)
__Connecting capacitors in parallel:__

(i) Connect the capacitors in parallel circuit. Adjust the power supply to supply 3 VDC by using a voltmeter.

(ii) Set the electrometer to read DC volts measuring V_{1}, V_{2} and V_{3} for each corresponding

capacitor. The values are recorded in the table.

(iii) Discharge each capacitor by touching the terminals wires of the capacitor to a metal before changing the voltage.

(iv) Repeat steps 2 and 3 for power supply voltages of 5 VDC and 10 VDC.

**TABULATION OF DATA:**

Table 1 – Capacitors

C_{1} (D) |
C_{2} D) |
_{3}D) |

Table 2 – Measurements of the voltages of the capacitors in series circuit

V (volts) |
V_{1} (volts) |
V_{2} (volts) |
V_{3} (volts) |

Table 3 – Measurements of the voltages of the capacitors in parallel circuit.

V (volts) |
V_{1} (volts) |
V_{2} (volts) |
V_{3} (volts) |

Table 4 – Calculation of Q for each capacitor in series circuit.

Q_{1} = (C_{1}V_{1}) |
Q_{2} = (C_{2}V_{2}) |
Q_{3} = (C_{3}V_{3}) |
Q = (C_{equivalent}V) |

Table 5 – Calculation of Q for each capacitor in parallel circuit.

Q_{1} = (C_{1}V_{1}) |
Q_{2} = (C_{2}V_{2}) |
Q_{3} = (C_{3}V_{3}) |
Q = (C_{equivalent}V) |

**COMPUTATIONS:**

**Calculation of Q for each capacitor in series circuit at 3 VDC:**

Q_{1} = (C_{1}V_{1}) =

Q_{2} = (C_{2}V_{2}) =

Q_{3} = (C_{3}V_{3}) =

1/C_{equiv} = 1/C_{1} + 1/C_{2} + 1/C_{3}

1/C_{equiv} =

1/C_{equiv} =

C_{equiv} =

V = V_{1} +V_{2} + V_{3}

V =

Q = (C_{equivalent}V) =

**At 5 VDC:**

Q_{1} = (C_{1}V_{1}) =

Q_{2} = (C_{2}V_{2}) =

Q_{3} = (C_{3}V_{3}) =

1/C_{equiv} = 1/C_{1} + 1/C_{2} + 1/C_{3}

1/C_{equiv} =

1/ C_{equiv} =

C_{equiv} =

V = V_{1} +V_{2} + V_{3}

V =

Q = (C_{equivalent}V) =

**At 10 VDC:**

Q_{1} = (C_{1}V_{1}) =

Q_{2} = (C_{2}V_{2}) =

Q_{3} = (C_{3}V_{3}) =

1/C_{equiv} = 1/C_{1} + 1/C_{2} + 1/C_{3}

1/C_{equiv} =

1/ C_{equiv} =

C_{equiv} =

V = V_{1} +V_{2} + V_{3}

V =

Q = (C_{equivalent}V) =

**Calculation of Q for each capacitor in parallel circuit**

**At 3 VDC:**

Q_{1} = (C_{1}V_{1}) =

Q_{2} = (C_{2}V_{2}) =

Q_{3} = (C_{3}V_{3}) =

C_{equiv}V = C_{1}V + C_{2}V + C_{3}V

V = V_{1} = V_{2} = V_{3} =

C_{equiv} = C_{1} + C_{2} + C_{3}

C_{equiv} =

Q = (C_{equiv}V) =

**At 5 VDC:**

Q_{1} = (C_{1}V_{1}) =

Q_{2} = (C_{2}V_{2}) =

Q_{3} = (C_{3}V_{3}) =

C_{equiv}V = C_{1}V + C_{2}V + C_{3}V

V = V_{1} = V_{2} = V_{3} =

C_{equiv} = C_{1} + C_{2} + C_{3}

C_{equiv} =

Q = (C_{equiv}V) =

**At 10 VDC:**

Q_{1} = (C_{1}V_{1}) =

Q_{2} = (C_{2}V_{2}) =

Q_{3} = (C_{3}V_{3}) =

C_{equiv}V = C_{1}V + C_{2}V + C_{3}V

V = V_{1} = V_{2} = V_{3} =

C_{equiv} = C_{1} + C_{2} + C_{3}

C_{equiv} =

Q = (C_{equiv}V) =