Question

A circuit with a combination of capacitors (each $1\times10^{-13}$ F) connected to a 1.5V battery is provided. Which capacitor maintains the highest potential difference? What is the potential difference? Which capacitor stores the highest amount of energy? Why? Fig. 4 Mixed combination Calculate the total amount of charge and energy stored in this combination. d) How will the total capacitance and the energy stored change if $C_1$ is removed? Support your answer. e) Will the total capacitance change if the capacitors are connected to a 3V battery instead of 1.5V? Support your answer. The following problems refer to Fig. 4; selected capacitors will have a variable capacitance; thus, answering these will involve the techniques of evaluating limits. Tips for handling the process: $\bullet$ show the initial algebraic expressions for $C_r$ (the total capacitance) $\bullet$ identify constant quantities and the quantity that changes $\bullet$ Identify the resulting algebraic function (rational or polynomial) $\bullet$ Evaluate the expressions by lugging in either 0 or infinity for the variable capacitor. a) Suppose that $C_1$ and $C_2$ have constant capacitance by $C_3$ has a variable capacitance. $\bullet$ What is $C_r$ if $C_3 \to \infty$? $\bullet$ What is $C_r$ if $C_3 \to 0$? b) Suppose that $C_1$ and $C_3$ have constant capacitances by $C_2$ has a variable capacitance. $\bullet$ What is $C_r$ if $C_2 \to 0$? $\bullet$ What is $C_r$ if $C_2 \to \infty$?

          A circuit with a combination of capacitors (each $1\times10^{-13}$ F) connected to a 1.5V battery is provided.
Which capacitor maintains the highest potential difference? What is the potential
difference?
Which capacitor stores the highest amount of energy? Why?
Fig. 4 Mixed combination
Calculate the total amount of charge and energy stored in this combination.
d) How will the total capacitance and the energy stored change if $C_1$ is removed?
Support your answer.
e) Will the total capacitance change if the capacitors are connected to a 3V battery instead of 1.5V? Support your answer.
The following problems refer to Fig. 4; selected capacitors will have a variable capacitance; thus, answering these will involve the
techniques of evaluating limits. Tips for handling the process:
$\bullet$ show the initial algebraic expressions for $C_r$ (the total capacitance)
$\bullet$ identify constant quantities and the quantity that changes
$\bullet$ Identify the resulting algebraic function (rational or polynomial)
$\bullet$ Evaluate the expressions by lugging in either 0 or infinity for the variable capacitor.
a) Suppose that $C_1$ and $C_2$ have constant capacitance by $C_3$ has a variable capacitance.
$\bullet$ What is $C_r$ if $C_3 \to \infty$?
$\bullet$ What is $C_r$ if $C_3 \to 0$?
b) Suppose that $C_1$ and $C_3$ have constant capacitances by $C_2$ has a variable capacitance.
$\bullet$ What is $C_r$ if $C_2 \to 0$?
$\bullet$ What is $C_r$ if $C_2 \to \infty$?

A circuit with a combination of capacitors (each 1×10^-13 F) connected to a 1.5V battery is provided.
Which capacitor maintains the highest potential difference? What is the potential
difference?
Which capacitor stores the highest amount of energy? Why?
Fig. 4 Mixed combination
Calculate the total amount of charge and energy stored in this combination.
d) How will the total capacitance and the energy stored change if C1 is removed?
Support your answer.
e) Will the total capacitance change if the capacitors are connected to a 3V battery instead of 1.5V? Support your answer.
The following problems refer to Fig. 4; selected capacitors will have a variable capacitance; thus, answering these will involve the
techniques of evaluating limits. Tips for handling the process:
∙ show the initial algebraic expressions for Cr (the total capacitance)
∙ identify constant quantities and the quantity that changes
∙ Identify the resulting algebraic function (rational or polynomial)
∙ Evaluate the expressions by lugging in either 0 or infinity for the variable capacitor.
a) Suppose that C1 and C2 have constant capacitance by C3 has a variable capacitance.
∙ What is Cr if C3 →∞?
∙ What is Cr if C3 → 0?
b) Suppose that C1 and C3 have constant capacitances by C2 has a variable capacitance.
∙ What is Cr if C2 → 0?
∙ What is Cr if C2 →∞?

Added by Keith J.

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