359316
Effective capacitance between \(A\) and \(B\) in the figure shown below is (all capacitances are in \(\mu F\,)\)
1 \(\frac{3}{{14}}{\text{ }}\mu F\)
2 \(\frac{{14}}{3}{\text{ }}\mu F\)
3 \(21{\text{ }}\mu F\)
4 \(23{\text{ }}\mu F\)
Explanation:
The points \(C\) and \(D\) will be at same potentials, since \(\dfrac{3}{6}=\dfrac{4}{8}\). Therefore, capacitance of \(2 \mu F\) will be ineffective. So, the equivalent circuit can be shown as the effective capacitance in upper arm in series, is given by
\({C_1} = \frac{{3 \times 6}}{{3 + 6}} = \frac{{18}}{9} = 2\mu F\) The effective capacitance in lower arm in series, is given by \(C_{2}=\dfrac{4 \times 8}{4+8}=\dfrac{32}{12}=\dfrac{8}{3} \mu F\) Hence, the resultant capacitance in parallel is given by \(\begin{aligned}C & =C_{1}+C_{2} \\& =2+\dfrac{8}{3}=\dfrac{14}{3} \mu F\end{aligned}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE
359317
In the figure, the equivalent capacitance between \(A\) and \(B\) is
1 \(3.75{\text{ }}\mu F\)
2 \(5.25{\text{ }}\mu F\)
3 \(6.5{\text{ }}\mu F\)
4 \(10.5{\text{ }}\mu F\)
Explanation:
The circuit can be simplified as shown in the figure below.
359316
Effective capacitance between \(A\) and \(B\) in the figure shown below is (all capacitances are in \(\mu F\,)\)
1 \(\frac{3}{{14}}{\text{ }}\mu F\)
2 \(\frac{{14}}{3}{\text{ }}\mu F\)
3 \(21{\text{ }}\mu F\)
4 \(23{\text{ }}\mu F\)
Explanation:
The points \(C\) and \(D\) will be at same potentials, since \(\dfrac{3}{6}=\dfrac{4}{8}\). Therefore, capacitance of \(2 \mu F\) will be ineffective. So, the equivalent circuit can be shown as the effective capacitance in upper arm in series, is given by
\({C_1} = \frac{{3 \times 6}}{{3 + 6}} = \frac{{18}}{9} = 2\mu F\) The effective capacitance in lower arm in series, is given by \(C_{2}=\dfrac{4 \times 8}{4+8}=\dfrac{32}{12}=\dfrac{8}{3} \mu F\) Hence, the resultant capacitance in parallel is given by \(\begin{aligned}C & =C_{1}+C_{2} \\& =2+\dfrac{8}{3}=\dfrac{14}{3} \mu F\end{aligned}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE
359317
In the figure, the equivalent capacitance between \(A\) and \(B\) is
1 \(3.75{\text{ }}\mu F\)
2 \(5.25{\text{ }}\mu F\)
3 \(6.5{\text{ }}\mu F\)
4 \(10.5{\text{ }}\mu F\)
Explanation:
The circuit can be simplified as shown in the figure below.
