A current of 2A flows through a 2$\mathrm{\Omega }$ resistor

when connected across a battery. The same

battery supplies a current of 0.5 A when

connected across a 9$\mathrm{\Omega }$ resistor. The internal

resistance of the battery is 

(1) $1/3\mathrm{\Omega }$                   

(2) $1/4\mathrm{\Omega }$

(3) $1\mathrm{\Omega }$                       

(4) $0.5\mathrm{\Omega }$

A galvanometer of resistance, G is shunted by a resistance S ohm. To keep the main current in the circuit unchanged, the resistance to be put in series with the galvanometer is

(1) $\frac{S^{\mathit{2}}}{(S+G)}$                                             

(2) $\frac{SG}{(S+G)}$

(3) $\frac{G^{\mathit{2}}}{(S+G)}$                                             

(4) $\frac{G}{(S+G)}$

Which one of the following bonds produces a solid that reflects light in the visible region and whose electrical conductivity decreases with temperature and has high melting point?

(1) metallic bonding

(2) van der Waals'bonding

(3) ionic bonding 

(4) covalent bonding

A potentiometer circuit is set up as shown.The potential gradient across the potentiometer wire, is k volt/cm and the ammeter, present in the circuit, reads 1.0A when two way key is switched off. The balance points, when the key between the terminals (i) 1 and 2 (ii) 1and 3, is plugged in, are found to be at lengths $l_{1}cm and l_{2}cm$ respectively.The magnitudes, of the resistors R and X, in ohm, are then, equal, respectively, to

(a)$k\left(l_2-l_1\right) and k{l}_2$

(b)$k{l}_1 and k\left(l_2-l_1\right)$

(c)$k\left(l_2-l_1\right)and k{l}_1$

(d)$k{l}_1 and k{l}_2$

A galvanometer has a coil of resistance $100\Omega$ and gives a full scale deflection for 30 mA current.If it is to work as a voltmeter of 30V range, the resistance required to be added will be 

(1) 900 $\Omega$                                     

(2) 1800 $\Omega$

(3) 500 $\Omega$                                     

(4) 1000 $\Omega$

A series combination of \(n_1\) capacitors, each of value \(C_1\), is charged by a source of potential difference \(4\) V. When another parallel combination of \(n_2\) capacitors, each of value \(C_2\), is charged by a source of potential difference \(V\), it has the same (total) energy stored in it as the first combination has. The value of \(C_2\) in terms of \(C_1\) is:
1. \(\frac{2C_1}{n_1n_2}\)
2. \(16\frac{n_2}{n_1}C_1\)
3. \(2\frac{n_2}{n_1}C_1\)
4. \(\frac{16C_1}{n_1n_2}\)

 Consider the following two statements :

(1) Kirchhoff's junction law follows from the conservation of charge.

(2) Kirchhoff's loop law follows from the conservation of energy.

     Which of the following is correct?

(a) Both (A) and (B) are wrong

(b) (A) is correct and (B) is wrong

(3) (A)  is wrong and (B) is correct

(4) Both (A) and (B) are correct

                         
1. \(0.6\pi~\Omega\)
2. \(3~\Omega\)
3. \(6\pi~\Omega\)
4. \(6~\Omega\)

A student measures the terminal potential difference \((V)\) of a cell (of emf \(\varepsilon \)$$ and internal resistance \(r\)) as a function of the current \((I)\) flowing through it. The slope and intercept of the graph between \(V\) and \(I,\) then respectively, equal:
1. \(\varepsilon \) and \(-r\)
2. \(-r\) and \(\varepsilon \)
3.   \(r\) and \(-\varepsilon \)
4. \(-\varepsilon \) and \(r\)

A galvanometer having a coil resistance of $60\Omega$ shows full scale deflection when a current of 1.0A passes through it. It can be converted into an ammeter to read currents upto 5.0A by 

(a) putting in series resistance of 240$\Omega$

(b) putting in parallel resistance of 240$\Omega$

(c) putting in series resistance of 15$\Omega$

(d) putting in parallel resistance of 15$\Omega$