J J Science Academy

1) The graph shows variation of current against applied potential difference, of a wire. The resistance of the wire is

1) $(3.3 k "," ")$

2) $(6.6 k "," ")$

3) $(1.5 k "," ")$

4) $(9 k "," ")$

Hint: $$R=\frac{dV}{dI}=\frac{15-5}{(6-3) \times 10^{-3}}=\frac{10}{3} \times 10^{3} \Omega=3.3 k \Omega$$

2) In which region of V-I graph of a specimen, is the resistance negative?

1) OA

2) AB

3) BC

4) Both AB and BC

Hint: $$Slope = R = \frac{V}{I}$$ At any point between A and B , tangent drawn has negative slope. Hence resistance will be negative.

3) A metal rod is connected to a source of E.M.F. If it is compressed, so that its area of cross-section, increases by $(0.1 \%)$ , the current in it will

1) decrease by $(0.1 \%)$ .

Hint: $$i=\frac{V}{R} \Rightarrow i \propto \frac{1}{R}$$ On stretching or compressing, volume is conserved. $$\therefore R \propto \frac{1}{A^{2}} \Rightarrow i \propto A^{2}$$ As $(A \uparrow es by 0.1 \%)$ , $(i \uparrow es by (2 \times 0.1 %) = 0.2 \%)$

4) A wire, having a resistance of $(6 \Omega)$ per unit area per unit length and length of 3 m , is connected to a source of potential difference of 18 V . The current through the wire, if area of cross-section is $(6 cm^{2})$ , is

1) 0.3 mA

2) 1.2 mA

3) 0.5 mA

4) 0.6 mA

Hint: $(\rho = Resistance per unit area per unit length)$ $$=6 \Omega-m$$ $$V=iR=i(\frac{\rho L}{A})$$ $$=\frac{VA}{\rho L}=\frac{18 \times 6 \times 10^{-4}}{6 \times 3}=0.6 mA$$

5) When a potential difference of V is applied across the ends of a conductor of length L , diameter of cross section $(D)$ , and resistivity $(\rho)$ , the current through it is $(I)$ . The potential difference per unit length of the conductor is

1) $(\frac{4 I \rho}{\pi D^{2}})$

2) $(\frac{I \rho}{\pi D^{2}})$

3) $(\frac{\pi D^{2}}{4 I \rho})$

4) $(\frac{\pi D^{2}}{I \rho})$

Hint: $$V=iR=i(\frac{\rho L}{\pi D^{2} / 4})$$ $$\frac{V}{L}=\frac{4 I \rho}{\pi D^{2}}$$

6) In an experiment, to study Ohm's law, a potential difference of 5 V is connected across a $(10 \Omega)$ resistance. An ammeter is connected in series with the E.M.F. source to measure the current and a voltmeter is connected across the resistance to measure the potential difference. The ammeter and the voltmeter readings can be i i = 5

1) $(0.5 A, 5 V)$

2) $(0.52 A, 5.2 V)$

3) $(0.48 A, 4.5 V)$

4) $(0.5 A, 1 V)$

Hint: Ammeter has its own resistance. $\rho$ Total resistance in circuit increases

7) Select the CORRECT statement.

1) Both linear and non-linear resistances obey Ohm's law.

2) Non-linear resistance obeys Ohm's law but not the linear resistance.

3) Both linear and non-linear resistances do not obey Ohm's law.

4) Only linear resistance obeys Ohm's law.

Hint: Graph of Ohm's law is a straight line, characteristics of linear resistance is same.

8) A graph of potential difference between two points on a current carrying conductor and the distance between them is

1) parabola.

2) curve.

3) straight line.

4) circle.

Hint: