Question 1

Q1: A piece of wire of resistance $R$ is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combi...

Accepted Answer

Answer: (d) 25 Explanation: Let the initial resistance of the wire be $R$ and its length be $l$. Resistance is directly proportional to length. When the wire is cut into five equal parts, the length of each part becomes $l/5$. Therefore, the resistance of each of the five parts is: $$R_{	ext{part}}...

Question 2

Q10: How many $176 \Omega$ resistors (in parallel) are required to carry 5 A on a 220 V line?

Accepted Answer

Given: Voltage of the line, $V = 220 	ext{ V}$ Total current required, $I = 5 	ext{ A}$ Resistance of each resistor, $R = 176 \Omega$ To Find: The number of resistors required, $n$. Formula: First, we find the total equivalent resistance ($R_p$) required for the circuit using Ohm's law: $$R_p = \f...

Question 3

Q11: Show how you would connect three resistors, each of resistance $6 \Omega$, so that the combination has a resistance of (i) $9 \Omega$, (ii) $4 \Omega$...

Accepted Answer

Let the three resistors be $R_1 = 6 \Omega$, $R_2 = 6 \Omega$, and $R_3 = 6 \Omega$. (i) To get a total resistance of $9 \Omega$: This can be achieved by connecting two resistors in parallel and then connecting the third resistor in series with this parallel combination. 1.  Connect two resistors ($...

Question 4

Q12: Several electric bulbs designed to be used on a 220 V electric supply line, are rated 10 W. How many lamps can be connected in parallel with each othe...

Accepted Answer

Given: Voltage of the supply line, $V = 220 	ext{ V}$ Power rating of each bulb, $P = 10 	ext{ W}$ Maximum allowable current, $I_{	ext{max}} = 5 	ext{ A}$ To Find: The number of lamps ($n$) that can be connected in parallel. Formula: First, we calculate the current drawn by a single bulb using t...

Question 5

Q13: A hot plate of an electric oven connected to a 220 V line has two resistance coils A and B, each of $24 \Omega$ resistance, which may be used separate...

Accepted Answer

Given: Voltage of the supply line, $V = 220 	ext{ V}$ Resistance of coil A, $R_A = 24 \Omega$ Resistance of coil B, $R_B = 24 \Omega$ Formula: The current $I$ is calculated using Ohm's law: $I = \frac{V}{R_{	ext{eq}}}$, where $R_{	ext{eq}}$ is the equivalent resistance for each case. Case 1: Coil...

Question 6

Q14: Compare the power used in the $2 \Omega$ resistor in each of the following circuits: (i) a 6 V battery in series with $1 \Omega$ and $2 \Omega$ resist...

Accepted Answer

Circuit (i): a 6 V battery in series with $1 \Omega$ and $2 \Omega$ resistors Given: Voltage, $V = 6 	ext{ V}$ Resistors are in series: $R_1 = 1 \Omega$, $R_2 = 2 \Omega$. 1.  Calculate the total resistance:     $$R_s = R_1 + R_2 = 1 \Omega + 2 \Omega = 3 \Omega$$ 2.  Calculate the total current in...

Question 7

Q15: Two lamps, one rated 100 W at 220 V, and the other 60 W at 220 V, are connected in parallel to electric mains supply. What current is drawn from the l...

Accepted Answer

Given: Lamp 1 rating: Power $P_1 = 100 	ext{ W}$, Voltage $V_1 = 220 	ext{ V}$ Lamp 2 rating: Power $P_2 = 60 	ext{ W}$, Voltage $V_2 = 220 	ext{ V}$ Supply voltage, $V_{	ext{supply}} = 220 	ext{ V}$ To Find: Total current ($I_{	ext{total}}$) drawn from the line. Method 1: Calculating individ...

Question 8

Q16: Which uses more energy, a 250 W TV set in 1 hr, or a 1200 W toaster in 10 minutes?

Accepted Answer

Given: For the TV set: Power, $P_{TV} = 250 	ext{ W}$ Time, $t_{TV} = 1 	ext{ hr} = 3600 	ext{ s}$ For the toaster: Power, $P_{	ext{toaster}} = 1200 	ext{ W}$ Time, $t_{	ext{toaster}} = 10 	ext{ minutes} = 10 	imes 60 	ext{ s} = 600 	ext{ s}$ To Find: Which appliance uses more energy. Form...

Question 9

Q17: An electric heater of resistance $44 \Omega$ draws 5 A from the service mains for 2 hours. Calculate the rate at which heat is developed in the heater...

Accepted Answer

Given: Resistance of the heater, $R = 44 \Omega$ Current drawn, $I = 5 	ext{ A}$ Time, $t = 2 	ext{ hours}$ (This information is not needed to find the rate). To Find: The rate at which heat is developed in the heater. Concept: The rate at which heat is developed is the electrical power ($P$). For...

Question 10

Q18: Explain the following. (a) Why is the tungsten used almost exclusively for filament of electric lamps? (b) Why are the conductors of electric heating...

Accepted Answer

(a) Why is the tungsten used almost exclusively for filament of electric lamps? Tungsten is used for the filaments of electric lamps due to the following properties: 1.  High Melting Point: Tungsten has a very high melting point (approximately $3380^{\circ}$C). This allows the filament to be heated...

Question 11

Q2: Which of the following terms does not represent electrical power in a circuit? (a) $I^{2} R$ (b) $I R^{2}$ (c) VI (d) $V^{2} / R$

Accepted Answer

Answer: (b) $I R^{2}$ Explanation: Electrical power ($P$) is the rate at which electrical energy is consumed in a circuit. The basic formula for power is: $$P = V I$$ where $V$ is the potential difference and $I$ is the current. Using Ohm's law, $V = IR$, we can derive other forms of the power formu...

Question 12

Q3: An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power consumed will be - (a) 100 W (b) 75 W (c) 50 W (d) 25 W

Accepted Answer

Answer: (d) 25 W Explanation: The resistance of the electric bulb's filament is constant. We can calculate this resistance from its power rating. Given (Rating): Rated Voltage, $V = 220 	ext{ V}$ Rated Power, $P = 100 	ext{ W}$ Formula: The relationship between power, voltage, and resistance is $P...

Question 13

Q4: Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across...

Accepted Answer

Answer: (c) 1:4 Explanation: Let the resistance of each of the two conducting wires be $R$. The potential difference across the combination is $V$. 1. Series Combination: When the wires are connected in series, the total resistance is: $$R_s = R + R = 2R$$ The heat produced ($H_s$) in time $t$ is gi...

Question 14

Q5: How is a voltmeter connected in the circuit to measure the potential difference between two points?

Accepted Answer

A voltmeter is always connected in parallel across the two points between which the potential difference is to be measured.  A voltmeter has a very high internal resistance. When connected in parallel, it draws a negligible amount of current from the main circuit. This ensures that the potential dif...

Question 15

Q6: A copper wire has diameter 0.5 mm and resistivity of $1.6 	imes 10^{-8} \Omega$ m. What will be the length of this wire to make its resistance $10 \O...

Accepted Answer

Part 1: Calculating the length of the wire Given: Diameter, $d = 0.5 	ext{ mm} = 0.5 	imes 10^{-3} 	ext{ m}$ Resistivity, $ho = 1.6 	imes 10^{-8} \Omega 	ext{ m}$ Resistance, $R = 10 \Omega$ To Find: Length of the wire, $l$ Formula: The resistance of a wire is given by $R = ho \frac{l}{A}$,...

Question 16

Q7: The values of current $I$ flowing in a given resistor for the corresponding values of potential difference $V$ across the resistor are given below - I...

Accepted Answer

Plotting the Graph: To find the resistance, we plot a graph of potential difference $V$ (on the y-axis) against current $I$ (on the x-axis). The data points are (0.5, 1.6), (1.0, 3.4), (2.0, 6.7), (3.0, 10.2), and (4.0, 13.2). The graph will be a straight line passing through the origin, which verif...

Question 17

Q8: When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistance of the resi...

Accepted Answer

Given: Potential difference, $V = 12 	ext{ V}$ Current, $I = 2.5 	ext{ mA} = 2.5 	imes 10^{-3} 	ext{ A}$ To Find: Resistance of the resistor, $R$ Formula: According to Ohm's law: $$V = IR$$ Therefore, the resistance $R$ can be calculated as: $$R = \frac{V}{I}$$ Calculation: $$R = \frac{12 	ext{...

Question 18

Q9: A battery of 9 V is connected in series with resistors of $0.2 \Omega, 0.3 \Omega, 0.4 \Omega, 0.5 \Omega$ and $12 \Omega$, respectively. How much cur...

Accepted Answer

Given: Voltage of the battery, $V = 9 	ext{ V}$ Resistances connected in series: $R_1 = 0.2 \Omega, R_2 = 0.3 \Omega, R_3 = 0.4 \Omega, R_4 = 0.5 \Omega, R_5 = 12 \Omega$. To Find: Current flowing through the $12 \Omega$ resistor. Concept: In a series circuit, the current is the same through every...

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