ANIMATED CHALKBOARD PRESENTATION

capacitor in the netwok given the capacitors connected in series/parallel

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Agenda:

• Determine the total charge,the charge on and the potential difference accross each capacitor connected in series/parallel.

• Show example on how to determine the total charged,Charge on and the potential difference accross in each capacitor in the network given the capacitors connected in series/parallel.

CAPACITOR:

A capacitor is an electronic component commonly used in electrical circuits to store and release electrical energy. It consists of two conductive plates separated by an insulating material called a dielectric. When a voltage is applied across the plates, an electric field is created, causing positive and negative charges to accumulate on the plates. To sum up, when capacitors are connected in series, their total capacitance decreases, while in parallel, their total capacitance increases. The voltage across capacitors is the same in both series and parallel connections, but the total charge stored varies depending on the configuration. These properties play a crucial role in designing electrical circuits and achieving the desired behavior for specific applications.

To determine the total charge, charge on each capacitor, and potential difference across each capacitor connected in series or parallel, we can use the following formulas and concepts:

1. Capacitors in Series: The total charge (Q_total) stored in capacitors connected in series is the same across all the capacitors. The charge on each capacitor (Q) can be calculated using the formula: Q = C × V, where C represents the capacitance of the capacitor and V is the applied voltage. The potential difference (V_cap) across each capacitor is different and can be calculated using the formula: V_cap = Q / C, where Q is the total charge and C is the capacitance of the specific capacitor. 2.Capacitors in Parallel: The total charge (Q_total) stored in capacitors connected in parallel is the sum of the charges on each individual capacitor. The charge on each capacitor (Q) is proportional to its capacitance in a parallel configuration. The formula for the charge on each capacitor is: Q = C × V, where C represents the capacitance of the specific capacitor and V is the applied voltage. The potential difference (V_cap) across each capacitor connected in parallel is the same and equal to the applied voltage (V).*

To determine the total charge across each capacitor connected in series or parallel, we can use the following guidelines:

1.Capacitors in Series:

• When capacitors are connected in series, the total charge (Q_total) stored in the series combination is the same for all capacitors.
• To find the total charge, we need to calculate the equivalent capacitance (C_total) of the series combination.
• The total charge can be calculated using the formula: Q_total = C_total × V, where C_total is the equivalent capacitance of the series combination and V is the applied voltage.
• Since the total charge is the same for all capacitors in series, each capacitor will have the same charge.

• 2.Capacitors in Parallel:
• When capacitors are connected in parallel, the total charge (Q_total) is the sum of the charges on each individual capacitor.
• The charge on each capacitor (Q) is proportional to its capacitance in a parallel configuration.
• The charge on each capacitor can be calculated using the formula: Q = C × V, where C is the capacitance of the specific capacitor and V is the applied voltage.
• The total charge across the parallel combination is the sum of the charges on each capacitor.

To determine the potential difference across each capacitor connected in series or parallel, we can use the following guidelines:

1.Capacitors in Series:

• When capacitors are connected in series, the total applied voltage (V_total) across the combination is divided among the individual capacitors.
• The potential difference across each capacitor in a series configuration is different.
• To find the potential difference across each capacitor, we can use the formula: V_cap = Q / C, where Q represents the charge stored on the capacitor and C is the capacitance of the specific capacitor.
• Since the charge on each capacitor is the same in a series configuration, we can use the formula: V_cap = Q_total / C, where Q_total is the total charge stored in the series combination and C is the capacitance of the specific capacitor.

2.Capacitors in Parallel:

• When capacitors are connected in parallel, the potential difference across each capacitor is the same and equal to the applied voltage (V).
• In a parallel configuration, the charge stored on each capacitor is different, but the potential difference across them remains the same.
• The potential difference across each capacitor connected in parallel is equal to the applied voltage.

To determine thecharge on across each capacitor connected in series or parallel, we can use the following guidelines:

1.Capacitors in Series:

• When capacitors are connected in series, the charge on each capacitor (Q) will be the same.
• The total charge (Q_total) stored in the series combination is divided among the capacitors.
• To find the charge on each capacitor, we can use the formula: Q = C × V, where C is the capacitance of the specific capacitor and V is the applied voltage.
• Since the charge is the same for all capacitors in series, each capacitor will have the same charge value.

2.Capacitors in Parallel:

• When capacitors are connected in parallel, the total charge (Q_total) stored in the combination is the sum of the charges on each individual capacitor.
• The charge on each capacitor (Q) in a parallel configuration will depend on its capacitance.
• The charge on each capacitor can be calculated using the formula: Q = C × V, where C is the capacitance of the specific capacitor and V is the applied voltage.
• The total charge across the parallel combination is the sum of the charges on each capacitor

REMEMBER;

The charge, potential difference, and capacitance values should be in consistent units (e.g., Coulombs, volts, and Farads, respectively). Using these concepts, you can determine the total charge, charge on each capacitor, and potential difference across each capacitor based on the configuration (series or parallel) and the given values of capacitance and voltage.

Let's go through an example to determine the totaL charge!

Example 1: Capacitors Connected in Series Suppose we have three capacitors connected in series with capacitances C1 = 2 μF, C2 = 4 μF, and C3 = 6 μF. The applied voltage across the series combination is V = 10 V.

1.Total Charge (Q_total):

• Since the capacitors are connected in series, the total charge stored in the series combination will be the same for all capacitors. We can calculate it using the formula:
• Q_total = C_total × V, where C_total is the equivalent capacitance of the series combination.
• To find C_total, we can use the formula for series capacitors:
• 1/C_total = 1/C1 + 1/C2 + 1/C3
• = 1/2x10^-6 + 1/4x10^-6 + 1/6x10^-6
• = (0.5x10^-6)+(0.25x10^-6)+(0.16667x10^-6)
• C_total = 9.1667x10^-7 F
• Now, we can calculate the total charge:
• Q_total = 9.1667x10^-7 F × 10 V = 9.1667x10^-6 F

2.Charge on Each Capacitor (Q):

Since the total charge is the same for all capacitors in series, the charge on each capacitor will be equal to Q_total. Q1 = Q2 = Q3 = 9.1667x10^-6 F

2.Charge on Each Capacitor (Q):

Since the total charge is the same for all capacitors in series, the charge on each capacitor will be equal to Q_total. Q1 = Q2 = Q3 = 9.1667x10^-6 F

3.Potential Difference (V_cap) across Each Capacitor:

The potential difference across each capacitor connected in series will be different. V_cap1 = Q1 / C1 = (9.1667x10^-6 F) / (2X10^-6F) = 4.58335V V_cap2 = Q2 / C2 = (9.1667x10^-6 F) / (4X10^-6F) = 2.291675V V_cap3 = Q3 / C3 = (9.1667x10^-6 F) / (6X10^-6F) = 1.527783V

The potential difference across each capacitor is approximately:

V1 = 4.58335V V2= 2.291675V V3= 1.527783V

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Example 2: Capacitors Connected in Parallel

Now, let's consider the same three capacitors connected in parallel with the same capacitances C1 = 2 μF, C2 = 4 μF, and C3 = 6 μF. The applied voltage across the parallel combination is V = 10 V.

1.Total Charge (Q_total): Since the capacitors are connected in parallel, the total charge stored in the parallel combination will be the sum of the charges on each capacitor.

• Q_total = C1 + C2 + C3
• = 2X10^-6 + 4X10^-6 + 6X10^-6
• Qtotal= 12X10^-6F

• We can calculate the charge on each capacitor using the formula Q = C × V:
• Q1 = C1 × V = 2X10^-6F × 10 V = 20X10^-6C
• Q2 = C2 × V = 4X10^-6F × 10 V = 40X10^-6C
• Q3 = C3 × V = 6X10^-6F × 10 V = 60X10^-6C

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2.Charge on Each Capacitor (Q): Since the capacitors are connected in parallel, the charge on each capacitor will be equal to the charge stored on that capacitor.

Since the capacitors are connected in parallel, the charge on each capacitor will be equal to the charge stored on that capacitor. Q1 = 20X10^-6C Q2 = 40X10^-6C Q3 = 60X10^-6C

3.Potential Difference (V_cap) across Each Capacitor:

The potential difference across each capacitor connected in parallel will be the same and equal to the applied voltage V. V_cap1 = V_cap2 = V_cap3 = 10 V

So, in summary, for the given series and parallel configurations: Series Configuration:

• Total charge (Q_total) = 9.1667x10^-6 F
• Charge on each capacitor (Q1 = Q2 = Q3) = 9.1667x10^-6 F
• Potential difference across each capacitor (V_cap1, V_cap2, V_cap3) = 4.58335V, 2.291675V, 1.527783V

Parallel Configuration:

• Total charge (Q_total) = 12X10^-6F
• Charge on each capacitor (Q1, Q2, Q3) = 20X10^-6C, 40X10^-6C, 60X10^-6C
• Potential difference across each capacitor (V_cap1 = V_cap2 = V_cap3) = 10 V

I hope this example helps clarify how to determine the total charge, charge on each capacitor, and potential difference across each capacitor in series and parallel configurations.