Potential and Potential Difference

Q. A parallel-plate capacitor has plates of area $200c{m}^2$ and separation between the plates $1mm$. The potential difference developed if a charge of $1nC(i.e.1\times {10}^{-9}C)$ is given to the capacitor is something, then if the plate separation is now increased to $2mm$, what will be the new potential difference?

Q. If $100volts$ of potential difference is applied between a and b in the circuit of given figure. Find the potential difference (in $V$) between c and d.

Q. An uncharged parallel-plate capacitor having a dielectric of dielectric constant $K$ is connected to a similar air cored parallel-plate capacitor charged to a potential $V_0$. The two share the charge and the common potential becomes $V$. The dielectric constant $K$ is

1. $\frac{V_0}{V}-1$
2. $\frac{V_0}{V}+1$
3. $\frac{V}{V_0}-1$
4. $\frac{V}{V_0}+1$

Q. A hemispherical earth plate is buried into the earth. Find the potential difference between the feet of a man standing on ground as shown in figure. Current through earth plate is I. Conductivity of earth is [$\delta ={10}^{-3}\pi ,I=1A$](up to two decimal places)

Q. A parallel-plate capacitor has plates of area $A$ and separation $d$ and is charged to a potential difference $V$. The charging battery is then disconnected and the plates are pulled apart until their separation is $2d$. What is the work required to separate the plates?

1. $\frac{3{\in }_{0}A{V}^2}{2d}$
2. $\frac{2{\in }_{0}A{V}^2}{d}$
3. $\frac{{\in }_{0}A{V}^2}{d}$
4. $\frac{{\in }_{0}A{V}^2}{2d}$

Q. The work done in increasing the potential of a capacitor from $V$ volt to $2V$ volt is $W$. Then, the work done in increasing the potential of the same capacitor from $2V$ volt to $4V$ volt will be

1. $W$
2. $2W$
3. $4W$
4. $8W$

Q. The work done on the capacitor is QV but the energy stored in the capacitor is 1/2QV. Why? By neglecting the resistance.

Q. A $10\mu F$ capacitor charged to $20V$ is connected across a $15V$ battery through a switch such that positive terminal of battery is connected to negative charged plate of capacitor. When switch is closed, work done by battery of $15V$ in long time will be

1. $2250\mu J$
2. $-3000\mu J$
3. $30000\mu J$
4. $5250\mu J$

Q. Two metallic spheres of radii $1cm$ and $3cm$ are given charges of $-1\times {10}^{-2}C$ and $5\times {10}^{-2}C$ respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is

1. $2\times {10}^{-2}C$
2. $3\times {10}^{-2}C$
3. $4\times {10}^{-2}C$
4. $1\times {10}^{-2}C$

Q.

This section contains 1 Assertion-Reason type question, which has 4 choices (a), (b), (c) and (d) out of which ONLY ONE is correct.

इस खण्ड में 1 कथन-कारण प्रकार का प्रश्न है, जिसमें 4 विकल्प (a), (b), (c) तथा (d) दिये गये हैं, जिनमें से केवल एक सही है।

A : Electrostatic field lines are always perpendicular on a non-conducting surface.

A : स्थिरवैद्युत क्षेत्र रेखाऐं किसी अचालक पृष्ठ पर सदैव लम्बवत् होती हैं।

R : Inside a conductor, electrostatic potential does not vary.

R : किसी चालक के अन्दर, स्थिरवैद्युत विभव परिवर्तित नहीं होता है।

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं तथा (R), (A) का सही स्पष्टीकरण है
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं लेकिन (R), (A) का सही स्पष्टीकरण नहीं है
3. (A) is true but (R) is false
   
   (A) सही है लेकिन (R) गलत है
4. (A) is false but (R) is true
   
   (A) गलत है लेकिन (R) सही है