A 2 μF capacitor and a 4 μF capacitor are connected in series, and this combination is connected in parallel with a 3 μF capacitor across a 12 V battery. The charge on the 4 μF capacitor is:

A
32 μC
B
24 μC
C
36 μC
D
16 μC

Q128. AI-generated practice Single-correct MCQ Medium

n identical capacitors, each of capacitance C, are first connected in series and then in parallel. The ratio of the parallel equivalent capacitance to the series equivalent capacitance is:

A
n
B
2n
C1/n²
Dn²

Q129. AI-generated practice Single-correct MCQ Hard

A 3 μF capacitor charged to 100 V and a 2 μF capacitor charged to 50 V are connected with their positive plates joined together and negative plates joined together. The common potential is:

A
80 V
B
60 V
C
40 V
D
75 V

Q130. AI-generated practice Single-correct MCQ Hard

A 3 μF capacitor charged to 100 V and a 2 μF capacitor charged to 50 V are connected with the positive plate of each joined to the negative plate of the other. The common potential is:

A
50 V
B
40 V
C
20 V
D
80 V

Q131. AI-generated practice Single-correct MCQ Medium

Treating the Earth as an isolated conducting sphere of radius 6.4 × 10⁶ m, its capacitance is about (1/(4πε₀) = 9 × 10⁹ N m² C^-2):

A
711 μF
B
71 nF
C
7.11 F
D
711 pF

Q132. AI-generated practice Single-correct MCQ Easy

One farad is equal to:

A
one coulomb per metre
B
one volt per coulomb
C
one joule per coulomb
D
one coulomb per volt

Q133. AI-generated practice Single-correct MCQ Medium

A 10 μF capacitor and a 5 μF capacitor are connected in series across a 30 V supply. The potential difference across the 5 μF capacitor is:

A
20 V
B
10 V
C
30 V
D
15 V

Q134. AI-generated practice Single-correct MCQ Hard

A metal slab of thickness d/2 is inserted between the plates of a parallel-plate capacitor of capacitance C and plate separation d, without touching the plates. The new capacitance is:

A
4C
B
3C/2
C
2C
D
C/2

Q135. AI-generated practice Numerical value Easy

A 6 μF capacitor is connected in series with a parallel combination of 2 μF and 4 μF capacitors. Find the equivalent capacitance (in μF).

Q136. AI-generated practice Numerical value Medium

A 2 μF and a 3 μF capacitor are connected in series across a 10 V battery. Find the charge (in μC) on the 2 μF capacitor.

Q137. AI-generated practice Numerical value Medium

A parallel-plate air capacitor is to have a capacitance of 1 nF with a plate separation of 0.885 mm. Take ε₀ = 8.85 × 10^-12 C² N^-1 m^-2. Find the required plate area in cm².

Q138. AI-generated practice Numerical value Hard

A 4 μF capacitor charged to 60 V is connected across an uncharged 2 μF capacitor. Find the loss of electrostatic energy, in units of 10^-1 mJ.

Q139. AI-generated practice Assertion–Reason Medium

Assertion (A): The capacitance of a parallel-plate capacitor does not depend on the charge on its plates.
Reason (R): The charges on the two plates of a charged capacitor are equal and opposite.

A
Both A and R are true and R is the correct explanation of A
B
Both A and R are true but R is not the correct explanation of A
C
A is true but R is false
D
A is false but R is true

Q140. AI-generated practice Assertion–Reason Hard

Assertion (A): When capacitors are connected in parallel, the equivalent capacitance is less than the smallest individual capacitance.
Reason (R): In a parallel combination all capacitors have the same potential difference.

A
Both A and R are true and R is the correct explanation of A
B
Both A and R are true but R is not the correct explanation of A
C
A is true but R is false
D
A is false but R is true