In a meter bridge experiment, the null point is at a distance of \(30~\text{cm}\) from \(\mathrm{A}\). If a resistance of \(16~\Omega\) is connected in parallel with resistance \(Y\), the null point occurs at \(50~\text{cm}\) from \(\mathrm{A}\). The value of the resistance \(Y\) is:
   
1. \(\frac{112}{3}~\Omega\)
2.  \(\frac{40}{3}~\Omega\)
3.  \(\frac{64}{3}~\Omega\)
4.  \(\frac{48}{3}~\Omega\)

In a potentiometer circuit, a cell of emf \(1.5~\text{V}\) gives a balance point at 36 cm length of wire. If another cell of emf 2.5 V replaces the first cell, then at what length of the wire, the balance point occur? 
1. 64 cm 
2. 62 cm 
3. 60 cm 
4. 21.6 cm

A resistance wire connected in the left gap of a meter bridge balances a \(10~\Omega\) $$ resistance in the right gap at a point which divides the bridge wire in the ratio \(3:2\). lf the length of the resistance wire is \(1.5~\text{m}\), then the length of \(1~\Omega\) of the resistance wire will be:
1. \(1.0\times 10^{-1}~\text{m}\) 
2. \(1.5\times 10^{-1}~\text{m}\)
3. \(1.5\times 10^{-2}~\text{m}\)
4. \(1.0\times 10^{-2}~\text{m}\)

The metre bridge shown is in a balanced position with \(\frac{P}{Q} = \frac{l_1}{l_2}\). If we now interchange the position of the galvanometer and the cell, will the bridge work? If yes, what will be the balanced condition?

    
1. Yes, \(\frac{P}{Q}=\frac{l_1-l_2}{l_1+l_2}\)
2. No, no null point
3. Yes, \(\frac{P}{Q}= \frac{l_2}{l_1}\)
4. Yes, \(\frac{P}{Q}= \frac{l_1}{l_2}\)