Potential and Potential Difference

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. This section contains 1 Assertion-Reason type question, which has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A : Capacitance of a system is proportional to the magnitude of charge.
R : Charge on a capacitor is proportional to the potential difference.
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 : किसी निकाय की धारिता, आवेश के परिमाण के समानुपाती होती है।
R : किसी संधारित्र पर आवेश, विभवान्तर के समानुपाती होता है।

1. (A) is true but (R) is false
   (A) सही है लेकिन (R) गलत है
2. (A) is false but (R) is true
   (A) गलत है लेकिन (R) सही है
3. 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
4. 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

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. 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. $5250\mu J$