Potentiometer, Cell & their Combinations

1 Mark Questions

1.State the underlying principle of a potentiometer? [Delhi 2014 c]

Ans. The potentiometer works on the principle that potential difference across any two points of uniform current carrying conductor is directly proportional to the length between the two points.

2.Two identical cells, each of emf E, having negligible internal resistance, are connected in parallel with each other across an external resistance What is the current through this resistance? [All India 2013]

Ans. The cells are arranged as shown in the circuit Ε ₩₩ R As the internal resistance of cells is negligible, so total resistance of the circuit = R So. current through the resistance. I=E/R (In parallel combination, potential is same as the single cell)

3. A 10 V battery of negligible internal resistance is connected across a 200 V battery and a resistance of 38 <math>\Omega</math> as shown in the figure. Find the value of the current in circuit.

10 V

₩₩ <math>38 \Omega</math> 200 V

[Delhi 2013]

Ans. Since, the positive terminal of the batteries are connected together, so the equivalent emf of the batteries is given by £ = <math>200 - 10 = 190 \text{ V}</math>

Hence, the current in the circuit is given by I=E/R=190/38=5 A

1. The emf of a cell is always greater than its terminal voltage. Why? Give reason. [Delhi 2013]

Ans. The emf of a cell is greater than its terminal voltage because there is some potential drop across the cell due to its small internal resistance

5.A cell of emf E and internal resistance r draws a current Write the relation between terminal voltage V in terms of E, I and r.[Delhi 2013]

Ans. When a current Idraws from a cell of emf E and internal resistance r, then the terminal voltage is

<math>V = E - Ir</math>.

6.A resistance R is connected across a cell of emf E and internal resistance r. Now, a potentiometer measures the potential difference between the terminals of the cells as V. Write the expression for r in terms of E, V and R.

[Delhi 2011, 2010]

Ans.

Internal resistance, <math>r = R\left(\frac{E}{V} - 1\right)</math>

where, signs are as usual.

7.A (i) series (ii) parallel combination of two given resistors is connected, one-by-one, across a cell. In which case, will the terminal potential difference across the cell have a higher value?[All India 2008 C]

Ans. The equivalent resistance combination of resistances is (i) greater than the greatest resistance in series combination and (ii) smaller than the least value of resistance in parallel combination.

The terminal potential difference across the cell is higher in series combination as <math>V = E -</math> Ir and due to higher resistance, current I is less in series combination.

1. The plot of the variation of potential difference across a combination of three identical

cells in series versus current is as shown in figure. What is the emf of each cell? V 6 V

0 1 A [Delhi 2008]

Ans.Terminal potential difference across a cell can be obtained by subtracting potential drop across internal resistance of the cell from the emf of the cell.

v Terminal voltage across cell combination, <math>V = E - Ir</math> when current I=0 => V = E From graph, when <math>I = 0</math>, <math>V = 6 V</math>

<math>=></math> emf E = 6 V

2 Marks Questions

9.A cell of emf E and internal resistance r is connected across a variable resistor Plot a graph showing variation of terminal voltage V of the cell versus the current I. Using the plot, show the emf of the cell and its internal resistance can be determined.[All India 2014] Ans.