2<\/sub>. The ratio of \\(\\frac{P_{2}}{P_{1}}\\) is
\na) 1
\nb) 2
\nc) 3
\nd) 4
\nAnswer:
\nd) 4
\nSolution:
\n<\/p>\nQuestion 8.
\nIn India electricity is supplied for domestic use at 220 V. It is supplied at 110 V in the USA. If the resistance of a 60W bulb for use in India is R, the resistance of a 60W bulb for use in the USA will be
\na) R
\nb) 2R
\nc) \\(\\frac{\\mathrm{R}}{4}\\)
\nd) \\(\\frac{R}{2}\\)
\nAnswer:
\nc) \\(\\frac{\\mathrm{R}}{4}\\)
\nSolution:
\n\\(P=\\frac{V^{2}}{R}\\)
\nIndia, V = 220V, P = 60W, R = R
\nUSA, V = 110V, P’ = 60W, R’ = ?
\n\u2234 R = \\(\\frac{\\mathrm{V}^{2}}{\\mathrm{P}}\\)
\nP = P’
\n\u2234 \\(\\mathrm{R}^{\\prime}=\\frac{\\mathrm{V}^{2}}{\\mathrm{~V}^{2}}=\\frac{110 \\times 110}{220 \\times 220}=\\frac{1}{4} \\quad {\\mathrm{R}^{\\prime}=\\frac{\\mathrm{R}}{4}}\\)<\/p>\n
Question 9.
\nIn a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W, and 1 heater of 1 kW are connected. The voltage of electric mains is 220 V. The minimum capacity of the main fuse of the building will be
\na) 14 A
\nb) 8 A
\nc) 10 A
\nd) 12 A
\nAnswer:
\nd) 12A
\nSolution:
\n<\/p>\n
Question 10.
\nThere is a current of 1.0 A in the circuit shown below. What is the resistance of P?
\n
\na) 1.5 \u03a9
\nb) 2.5 \u03a9
\nc) 3.5 \u03a9
\nd) 4.5 \u03a9
\nAnswer:
\nc) 3.5 \u03a9
\nSolution:
\nBy Kirchhoff\u2019s voltage law,
\n9 = (3 \u00d7 1) + (2.5 \u00d7 1) + (P \u00d7 1)
\n9 =3 + 2.5 + P
\n9 = 5.5 + P
\nP = 9 – 5.5
\nP = 3.5 \u03a9<\/p>\n
<\/p>\n
Question 11.
\nWhat is the current drawn out from the battery?
\n
\na) 1 A
\nb) 2 A
\nc) 3 A
\nd) 4 A
\nSolution:
\n<\/p>\n
Question 12.
\nThe temperature deficient of resistance of a wire is 0.00125 per\u00b0C At 20\u00b0C, its resistance is 1\u03a9. The resistance of the wire will be 2\u03a9 at
\na) 800\u00b0C
\nb) 700\u00b0C
\nc) 850\u00b0C
\nd) 820\u00b0C
\nAnswer:
\nd) 820\u00b0C<\/p>\n
Question 13.
\nThe internal resistance of a 2.1 V cell which gives a current of 0.2 A through a resistance of 10 \u03a9 is
\na) 0.2 \u03a9
\nb) 0.5 \u03a9
\nc) 0.8 \u03a9
\nd) 1.0 \u03a9
\nAnswer:
\nb) 0.5 \u03a9
\nSolution:
\n\\(r=\\left(\\frac{E-V}{V}\\right) R\\)
\nE = 2.1 V
\nV = IR = 0.2 \u00d7 10
\nV = 2 V
\n\\(\\begin{aligned}
\nr &=\\left(\\frac{2.1-2}{2}\\right) 10 \\\\
\n&=\\frac{0.1}{2} \\times 10
\n\\end{aligned}\\)
\nr = 0.5 \u03a9<\/p>\n
Question 14.
\nA piece of copper and another of germanium are cooled from room temperature to 80 K. The resistance of
\na) each of them increases
\nb) each of them decreases
\nc) copper increases and germanium decreases
\nd) copper decreases and germanium increases
\nAnswer:
\nd) copper decreases and germanium increases
\nSolution:
\nCopper is a positive temperature coefficient of resistance, i.e their resistance decreases with a decrease in temperature. Germanium is a negative temperature coefficient of resistance, i.e their resistance increases with a decrease in temperature.<\/p>\n
Question 15.
\nIn Joule\u2019s heating law, when R and t are constant, if the H is taken along the y axis and I2<\/sup> along the x-axis, the graph is _______
\na) straight line
\nb) parabola
\nc) circle
\nd) ellipse
\nAnswer:
\na) straight line
\nSolution:
\nH = I2<\/sup>RT
\nH \u03b1 I2<\/sup>
\n\u2234 The graph is a straight line.<\/p>\n<\/p>\n
II. Short Answer Questions:<\/span><\/p>\nQuestion 1.
\nWhy current is a scalar?
\nAnswer:
\nThe current I is defined as the scalar product of current density and area vector in which the charges cross.
\nI = \\(\\vec { j } \\) . \\(\\vec { A } \\)
\nThe dot product of two vector quantity is a scalar form. Hence, the current is called a scalar quantity.<\/p>\n
Question 2.
\nDefine Current density.
\nAnswer:
\nThe current density is defined as the current per unit area of the cross-section of the conductor.
\nJ = \\(\\mathrm{I} \/ \\mathrm{A}\\)
\nS.I unit is A\/m2<\/sup><\/p>\nQuestion 3.
\nDistinguish between drift velocity and mobility.
\nAnswer:
\n<\/p>\n
Question 4.
\nState microscopic form of Ohm\u2019s law.
\nAnswer:
\nThe macroscopic form of Ohm\u2019s Law relates voltage, current, and resistance. Ohm\u2019s Law states that the current through an object is proportional to the voltage across it and inversely proportional to the object\u2019s resistance.
\nV = IR.<\/p>\n
Question 5.
\nState macroscopic form of Ohm\u2019s law.
\nAnswer:
\nThe macroscopic form of Ohm\u2019s law is V = IR
\nWhere V \u2192 Potential difference
\nI \u2192 Current
\nR \u2192 Resistance.<\/p>\n
<\/p>\n
Question 6.
\nWhat are the ohmic and non-ohmic devices?
\nAnswer:
\nMaterials for which the current against voltage graph is a straight line through the origin, are said to obey Ohm\u2019s law and their behaviour is said to be ohmic. Materials or devices that do not follow Ohm\u2019s law are said to be non-ohmic.<\/p>\n
Question 7.
\nDefine electrical resistivity.
\nAnswer:
\nThe electrical resistivity of a material is defined as the resistance offered to current flow by a conductor of unit length having a unit area of cross-section.
\n\\(\\rho=\\frac{R A}{L}\\)
\nIts unit is ohm-meter (\u03a9m)<\/p>\n
Question 8.
\nDefine temperature coefficient of resistance.
\nAnswer:
\nThe ability of certain metals, their compounds, and alloys to conduct electricity with zero resistance at very low temperatures is called superconductivity.<\/p>\n
Question 9.
\nWhat are superconductors?
\nAnswer:<\/p>\n
\n- The resistance of certain materials becomes zero below a certain temperature, known as critical or transition temperature.<\/li>\n
- The materials that exhibit this property are known as superconductors and the phenomenon is known as superconductivity.<\/li>\n<\/ol>\n
Question 10.
\nWhat are electric power and electric energy?
\nAnswer:<\/p>\n
\n\n\nElectric Energy<\/td>\n | Electric Power<\/td>\n<\/tr>\n |
\nElectric potential energy gained by the charge carries as they move through potential difference v is dw = v dQ<\/td>\n | Electric Power is the rate at which energy is transformed.<\/p>\n P = dw\/dt<\/td>\n<\/tr>\n |
\ndw = P dt<\/td>\n | P = VI<\/td>\n<\/tr>\n |
\nUnit: 1 kWh<\/td>\n | Unit: Watt<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n <\/p>\n Question 11. \nDerive the expression for power P = VI in an electrical circuit. \nAnswer: \nPower is defined as the rate at which the electrical potential energy is delivered. \n\\(\\begin{array}{l} \n<\/p>\n Question 12. \nWrite down the various forms of expression for power in electrical circuit. \nAnswer: \nThe electric power P is the rate at which the electrical potential energy is delivered, \nP = [latex]\\frac { dU }{ dt }\\) = \\(\\frac { 1 }{ dt }\\) (V.dQ) = V.\\(\\frac { dQ }{ dt }\\) \n[dU = V.dQ] \nThe electric power delivered by the battery to any electrical system. \nP = VI \nThe electric power delivered to the resistance R is expressed in other forms. \nP = VI = I(IR) = I2<\/sup>R \nP = IV = \\((\\frac { V }{ R })\\) V = \\(\\frac {{ V }^{2}}{ R }\\).<\/p>\nQuestion 13. \nState Kirchhoff\u2019s current rule. \nAnswer:<\/p>\n \n- Kirchhoff’s current rule states that the algebraic sum of the currents at any junction of a circuit is zero.
\ni.e \u03a3junction<\/sub> i = 0<\/li>\n- It is a statement of conservation of electric charge.<\/li>\n<\/ol>\n
Question 14. \nState Kirchhoff\u2019s voltage rule. \nAnswer: \nIt states that in a closed circuit the algebraic sum of the products of the current and resistance of each part of the circuit is equal to the total emf included in the circuit. This rule follows from the law of conservation of energy for an isolated system.<\/p>\n Question 15. \nState the principle of the potentiometer. \nAnswer: \nThe emf (E) of the cell is directly proportional to the balancing length (l) \n\u03be \u221d l \n\u03be = Irl \nWhere I \u2192current \nr \u2192 resistance per unit length of the wire.<\/p>\n <\/p>\n Question 16. \nWhat do you mean by the internal resistance of a cell? \nAnswer: \nThe resistance offered by the electrolyte of a cell to the flow of current between its electrodes is called internal resistance of the cell. An ideal battery has zero internal resistance and the potential difference across the battery equal to its emf. But a real battery is made of electrodes and electrolytes, there is resistance to the flow of charges within the battery. A freshly prepared cell has low internal resistance and it increases with aging.<\/p>\n Question 17. \nState Joule\u2019s law of heating. \nAnswer: \nThe heat developed in an electrical circuit due to the flow of current varies directly as<\/p>\n \n- the square of the current<\/li>\n
- the resistance of the circuit and<\/li>\n
- the time of flow H = I2<\/sup>Rt<\/li>\n<\/ul>\n
Question 18. \nWhat is the Seebeck effect? \nAnswer: \nSeebeck discovered that in a closed circuit consisting of two dissimilar metals, when the junctions are maintained at different temperatures, an emf (potential difference) is developed.<\/p>\n Question 19. \nWhat is the Thomson effect? \nAnswer:<\/p>\n \n- When two points in a conductor are at different temperatures, the density of electrons at these points will differ and as a result, me potential difference is created between these points.<\/li>\n
- This is known as the Thomson effect. Thomson effect is also reversible.<\/li>\n<\/ol>\n
Question 20. \nWhat is the Peltier effect? \nAnswer: \nWhen an electric current is passed through a circuit of a thermocouple, heat is evolved at one junction and absorbed at the other junction. This is known as the Peltier effect.<\/p>\n Question 21. \nState the applications of the Seebeck effect. \nAnswer:<\/p>\n \n- The Seebeck effect is used in thermoelectric generators (Seebeck generators). These thermoelectric generators are used in power plants to convert waste heat into electricity.<\/li>\n
- This effect is utilised in automobiles as automotive thermoelectric generators for increasing fuel efficiency.<\/li>\n
- The Seebeck effect is used in thermocouples and thermopiles to measure the temperature difference between the two objects.<\/li>\n<\/ol>\n
<\/p>\n III. Long Answer Questions:<\/span><\/p>\nQuestion 1. \nDescribe the microscopic model of current and obtain the general form of Ohm’s law. \nAnswer:<\/p>\n \n- XY is a conductor of an area of cross-section A<\/li>\n
- E is the applied electric field.<\/li>\n
- n is the number of electrons per unit volume with the same drift velocity (vd<\/sub>)<\/li>\n<\/ol>\n
Let electrons move through a distance dx in time interval dt. \n \nMicroscopic model of the current \n\u2234 \\(v d=\\frac{d x}{d t}\\) \ndx = vd<\/sub> . dt …………(1)<\/p>\nElectrons available in the given volume \n= volume \u00d7 number per unit volume \n= A. dx \u00d7 n \n= A . vd<\/sub> dt \u00d7 n [From (1)]<\/p>\nTotal charge in volume dQ = charge \u00d7 number of electrons \ndQ = (e) (Avd<\/sub> dt) n<\/p>\n<\/p>\n Question 2. \nObtain the macroscopic form of Ohm\u2019s law from its microscopic form and discuss its limitation. \nAnswer:<\/p>\n \n- Consider a segment of wire of length l and area of cross section A<\/li>\n
- Electric field is created when a potential difference V is applied<\/li>\n
- If \u2018E\u2019 is uniform, then, V = El<\/li>\n
- Current density, J = \u03c3 E = \u03c3\\(\\frac{\\mathrm{V}}{l}\\)<\/li>\n<\/ol>\n
Since J = \\(\\frac{\\mathrm{I}}{\\mathrm{A}}\\) \n\\(\\frac{\\mathrm{I}}{\\mathrm{A}}=\\sigma \\frac{\\mathrm{V}}{l}\\) \nRearranging the above equation, Current through the conductor<\/p>\n \n \nLimitations: \nThere are certain materials and devices where the proportionality of V and I does not hold good.<\/p>\n
Question 3. \nExplain the equivalent resistance of a series and parallel resistor network. \nAnswer: \nResistors in series: \n \n<\/p>\n \n- Let V1<\/sub>, V2<\/sub>, V3<\/sub> be the potential difference across R1<\/sub>, R2<\/sub>, R3<\/sub><\/li>\n
- In the series network, the current is the same.<\/li>\n
- The net potential difference V = V1<\/sub> + V2<\/sub> + V3<\/sub><\/li>\n
- By Ohm’s law: V1<\/sub> = IR1<\/sub>, V2<\/sub> = IR2<\/sub>, V3<\/sub>= IR3<\/sub><\/li>\n
- The equivalent resistance is RS<\/sub> and V = IRS<\/sub> in series.<\/li>\n
- IRS<\/sub> = IR1<\/sub> + IR2<\/sub> + IR3<\/sub><\/li>\n
- RS<\/sub> = R1<\/sub> + R2<\/sub> + R3<\/sub><\/li>\n
- The equivalent resistance is the sum of the individual resistances.<\/li>\n<\/ol>\n
Resistors in Parallel: \n \n<\/p>\n \n- In a parallel network, the potential difference across each resistor is the same.<\/li>\n
- current I is divided into I1<\/sub>, I2<\/sub>, I3<\/sub>, same that
\nI = I1<\/sub> + I2<\/sub> + I3<\/sub> ………..(1) \nBy ohm’s law \n<\/li>\n- In parallel network, the reciprocal of the equivalent resistance is equal to the sum of the reciprocal of the resistance of the individual resistors.<\/li>\n<\/ol>\n
<\/p>\n Question 4. \nExplain the determination of the internal resistance of a cell using voltmeter. \nAnswer:<\/p>\n \n- The emf of the cell \u03be is found by connecting a high resistance voltmeter across it. Without connecting the external resistance R.<\/li>\n
- Since the voltmeter draws very little current for deflection, the circuit is called an open circuit.<\/li>\n
- Voltmeter reading gives the emf of the cell.<\/li>\n
- Resistance \u2018R is included in the circuit and current I is established in the circuit.<\/li>\n
- The potential drop across the resistor.
\nR is V = IR …………(1)<\/li>\n - \u00a0Due to internal resistance (r) the voltmeter reads a value V, less than the emf of cell (E).<\/li>\n
- \u00a0V = \u03be – Ir<\/li>\n
- Ir = \u03be – V …………(2)<\/li>\n
- Dividing (2) by (1)
\n<\/li>\n - Internal resistance of the cell
\n\\(\\frac{\\mathrm{Ir}}{\\mathrm{IR}}=\\frac{\\xi-\\mathrm{V}}{\\mathrm{V}}\\) \n\\(\\mathrm{r}=\\left(\\frac{\\xi-\\mathrm{V}}{\\mathrm{V}}\\right) \\mathrm{R}\\)<\/li>\n - Since \u03be, V and R are known, internal resistance r can be calculated<\/li>\n<\/ol>\n
Question 5. \nState and explain Kirchhoff\u2019s rules. \nAnswer: \nKirchhoff\u2019s rules are used to find current and voltage for more complex circuits. There are 2 rules.<\/p>\n |