Physics Answer the following in Brief

A potentiometer wire has a length of \(4 m\) and a resistance of \(5 \Omega\). What resistance should be connected in series with a potentiometer wire and a cell of e.m.f. \(2 V\) having internal resistance \(1 \Omega\) to get a potential gradient of \(10^{-3} V / cm\) ?

Two cells of emf \(4 V\) and \(2 V\) having respective internal respective internal resistance of \(1 \Omega\) and \(2 \Omega\) are connected in parallel, in so to send current in the same direction through an external resistance of \(5 \Omega\). Find the current through the external resistance.

Two resistances \(X\) and \(Y\) in the two gaps of a meter-bridge gives a null point dividing the wire in the ratio \(2: 3\). If each resistance is increased by \(30 \Omega\), the null point divides the wire in the ratio \(5: 6\), calculate the value of \(X\) and \(Y\).

When a resistor of \(5 \Omega\) is connected across the cell, its terminal potential difference is balanced by \(150 cm\) of potentiometer wire and when a resistance of \(10 \Omega\) is connected across cell, the terminal potential difference is balanced by \(175 cm\) same potentiometer wire. Find the balancing length when the cell is in open circuit and the internal resistance of the cell.

A cell balances against a length of \(200 cm\) on a potentiometer wire, when it is shunted by a resistance of \(8 \Omega\). The balancing length reduces by \(40 cm\), when it is shunted by a resistance of \(4 \Omega\). Calculate the balancing length when the cell is in open circuit. Also calculate the internal resistance of the cell.

Explain with neat circuit diagram how will you determine unknown resistance by using meterbridge experiment.

Find the total current 'I' flowing through the following circuit.

When a resistance of \(12 ohm\) is connected across a cell, its terminal potential difference is balanced by \(120 cm\) length of potentiometer wire. When the resistance of \(18 ohm\) is connected across the same cell, the balancing length is \(150 cm\). Find the balancing length when the cell is in open circuit. Also calculate the internal resistance of the cell.

Explain the use of potentiometer to determine internal resistance of a cell.

Resistance of a potentiometer wire is \(0.1 \Omega / cm\). A cell of emf \(1.5 V\) is balanced at \(300 cm\) on this potentiometer wire. Calculate the current and balancing length for another cell of e.m.f. \(1.4 V\) on the same potentiometer wire.

Two diametrically opposite points of a metal ring are connected to two terminals of the left gap of meter bridge. The resistance of \(11 \Omega\) is connected in right gap. If null point is obtained at a distance of \(45 cm\) from the left end, find the resistance of metal ring.