Name: Electric Energy Density
Uploaded: 2019-07-19
Duration: 4 min 11 s
Description: There is an energy associated with the electrostatic field. The expression of this electric field energy density is derived using the energy stored in a para...

Question

Determine the potential difference $V_{A} - V_{B}$ between points $A$ and $B$ of the circuit shown in Figure below. Under what condition is it equal to zero?

Accepted Answer

$V (\frac{C_{2} C_{3} - C_{1} C_{4}}{(C_{1} + C_{2}) (C_{3} + C_{4})}), \frac{C_{1}}{C_{2}} = \frac{C_{3}}{C_{4}}$

Suppose the charge $q_{1}$ flows in the upper branch and $q_{2}$ in the lower branch.

$C_{1}$ and $C_{2}$ are connected in series, their equivalent capacitance of is

$\frac{1}{C_{5}} = \frac{1}{C_{1}} + \frac{1}{C_{2}}$

Potential difference across their equivalent capacitance is

$V = q_{1} (\frac{1}{C_{1}} + \frac{1}{C_{2}})$ or $q_{1} = \frac{V C_{1} C_{2}}{C_{1} + C_{2}}$

$C_{3}$ and $C_{4}$ are connected in series, their equivalent capacitance of is

$\frac{1}{C_{6}} = \frac{1}{C_{3}} + \frac{1}{C_{4}}$

The potential difference across their equivalent capacitance is

$V = q_{2} (\frac{1}{C_{3}} + \frac{1}{C_{4}})$

or $q_{2} = \frac{V C_{3} C_{4}}{C_{3} + C_{4}}$

$∴ V_{A} - V_{B} = (V_{Q} - V_{B}) - (V_{Q} - V_{A}) = \frac{q_{2}}{C_{4}} - \frac{q_{1}}{C_{2}}$

Putting the values of $q_{1}$ and $q_{2},$ we get

$V_{A} - V_{B} = \frac{V C_{3}}{C_{3} + C_{4}} - \frac{V C_{1}}{C_{1} + C_{2}}$

$V_{A} - V_{B} = V [\frac{C_{2} C_{3} - C_{1} C_{4}}{(C_{1} + C_{2}) (C_{3} + C_{4})}]$

For $V_{A} - V_{B} = 0$ ,the numerator of the $V_{A} - V_{B}$ will be zero.

$C_{2} C_{3} - C_{1} C_{4} = 0$

or $\frac{C_{1}}{C_{2}} = \frac{C_{3}}{C_{4}}$

Determine the potential difference $V_{A} - V_{B}$ between points $A$ and $B$ of the circuit shown in Figure below. Under what condition is it equal to zero?

Important Questions on Electrostatic Potential and Capacitance

Learn and Prepare for any exam you want !

Determine the potential difference VA-VB between points A and B of the circuit shown in Figure below. Under what condition is it equal to zero?

Important Questions on Electrostatic Potential and Capacitance

Learn and Prepare for any exam you want !

Determine the potential difference $V_{A} - V_{B}$ between points $A$ and $B$ of the circuit shown in Figure below. Under what condition is it equal to zero?