Q. What does an electric circuit mean?
Ans. A continuous conducting path consisting of wires and other electrical components (like resistance or electric bulb, switch etc.) between the two terminals of a cell or battery, along which an electric current flows, is called an electric circuit.
Q. What is meant by saying that the potential difference between two points is 1 V?
Ans. The potential difference between two points is said to be 1 volt if 1 joule of work is done in moving 1 coulomb of electric charge from one point to the other.
Q. Answer the following questions:
(i) Define electric power.
(ii) What is a super conductor? Give two examples.
(iii) What does an electric circuit mean?
(iv) Define conductors and insulators.
Ans. (i) The electrical work done per unit time is called electric power.
(ii) A superconductor is a substance of zero resistance at very low temperatures.
Example : Mercury below 4.2 K, Lead below 7.25 K.
(iii) A continuous conducting path consisting of wires and other electrical components (like resistance or electric bulb, switch etc.) between the two terminals of a cell or battery, along with an electric current flows, is called an electric circuit.
(iv) The substances through which electricity can flow are called conductors and the substances through which electricity cannot flow are called insulators.
Q. An electric lamp of 100 Ω, a toaster of resistance 50 Ω, and a water filter of resistance 500 Ω are connected in parallel to a 220 V source. What is the resistance of an electric iron connected to the same source that takes as much current as all three appliances and what is the current through it?
- Ans. The combined resistance R of the three electrical devices R_{1}, R_{2} and R_{3} connected in parallel is :
$$ \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$ Here, $$R_1 = 100 \Omega, R_2 = 50 \Omega \space and \space R_3 = 500\Omega $$ $$ \therefore \space \space \space \space \space \space \frac{1}{R} = \frac{1}{100} + \frac{1}{50} + \frac{1}{500} $$ $$ = \frac{5+10+1}{500}$$ $$ = \frac{16}{500}$$ or $$R = \frac{500}{16}$$ $$= 31.25\Omega $$ Thus, the resistance of electric iron is $$31.25\Omega $$
Now, Potential difference, V
= 220 V
Current, I = ?
$$ Resistance, R = 31.25 \Omega $$
$$ Using\space Ohm’s \space law \space : \space \frac{V}{I} = R$$ $$ or \space \space \space \space \space \frac{220}{I} = 31.25$$ $$ or \space \space \space \space \space I = \frac{220}{31.25}$$ $$ = 7.04 \space A$$
Hence, the current passing through the electric iron is 7.04 A.
Q. How can three resistors of resistances 2 Ω, 3 Ω and 6 W be connected to give a total resistance of (a) 4 Ω and (b) 1 Ω?
Ans. (a) The three resistors of resistances 2 Ω, 3 Ω and 6 Ω have to be combined as shown in the figure to obtain 4 Ω resistance. Equivalent resistance of 3 Ω and 6 Ω connected in parallel is,
$$\frac{1}{R_P} = \frac{1}{3} + \frac{1}{6}$$ $$ = \frac{2+1}{6} = \frac{3}{6}$$ or $$R_P = \frac{6}{3} = 2\Omega $$ $$Now, \space R_P \space and \space 2 \Omega \space are\space joined\space in\space series\space and\space the\space equivalent\space resistance\space is,$$ $$R = R_P + 2$$ $$= (2+2) \Omega $$ $$ = 4\Omega $$
(b) In order to obtain 1 Ω resistance, the resistors 2 Ω, 3 Ω and 6 Ω have to be combined as shown in figure. 2 Ω, 3 Ω and 6 Ω resistances are connected in parallel,
$$ \therefore \space \space \space \space \space \frac{1}{R} = \frac{1}{2} + \frac{1}{3} + \frac{1}{6}$$ $$= \frac{3+2+1}{6}$$ $$ = \frac{6}{6}$$ or $$R = 1 \Omega $$
Q. How many 176 W resistors in parallel are required to carry 5 A on a 220 V line?
- Ans. Here, Potential difference, V = 220 V, Current, I = 5 A
So, $$ \frac{1}{R_p} = \frac{1}{R_1}+\frac{1}{R_2}$$ $$ = \frac{1}{9} + \frac{1}{9} $$ $$= \frac{1+1}{9} = \frac{2}{9}$$ $$\frac{1}{R_p} = \frac{2}{9}$$ $$\frac{1}{R_p} = \frac{2}{9}$$ $$ R_P = \frac{9}{2} = 4.5 \Omega $$ Now, $$R_s = R_3 + 4.5 \Omega $$ $$= 9\Omega + 4.5 \Omega$$ $$ = 13.5 \Omega$$
(ii) To get equivalent resistance of 6 Ω, the resistance should be connected as shown in the given below
$$R_s = R_1 + R_2$$ $$= 9 + 9$$ $$= 18\Omega$$ Now both the resistance are in parallel with each other so,
$$R_P = \frac{1}{18} + \frac{1}{9}$$ $$ = \frac{1+2}{18} = \frac{3}{18}$$ $$= \frac{1}{6}W$$ So, $$R_P = 6 \Omega$$
Q. An electric iron of resistance 20 Ω takes a current of 5 A. Calculate the heat developed in 30 s.
- Ans. Here, Current (I) = 5 A, Resistance (R) = 20 Ω,
- Time (t) = 30 s
- Heat produced (H) = I^{2}Rt
- = (5)^{2} × 20 × 30
- = 15000 J
- Thus, heat developed is 1.5 × 10^{4} J.
Q. Which uses more energy, a 250 W T.V. set in 1 hour or a 1200 W toaster in 10 minutes?
- Ans. For T.V. Set : Power, P = 250 W
- Time, t = 1 h
- Electrical energy consumed = P × t
- = (250 x 1)/1000 kWh
- = 0.25 kWh
- For toaster : Power, P = 1200 W
- Time, t = 10 minutes
- = 10 h /60
- 1h/6
- Electrical energy consumed = P × t
- 1200 x 1 kWh/ 1000 x 6
- = 0.20 kWh
- The T.V. set uses more energy (0.25 kWh) whereas the toaster uses less energy (0.20 kWh).
Q. 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 resistor.
- Ans. Here, Potential difference, V = 12 V
Current, $$I \space = 2.5 \space mA = \frac{2.5}{1000}\space A = 0.0025 \space A$$
Using Ohm’s law
Resistance, $$R = \frac{V}{I} = \frac{12}{0.0025} = 4800 \space \Omega $$
Q. 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 line if the supply voltage is 220 V?
- Ans. Given: Power of one lamp, P_{1} = 100 W
- Power of second lamp, P_{2 }= 60 W
- Since, both the lamps are connected in parallel, thus,
- potential difference will be equal.
- Thus, Potential difference = 220 V
- We know, that Power (P) = VI
- Thus, the total cur rent through the circuit
$$I = \frac{P_1}{V} + \frac{P_2}{V}$$ $$I = \frac{100}{220} + \frac{60}{220}$$ $$ = \frac{100+60}{220} $$ $$ = \frac{160}{220} = 0.727 \space A$$
Q. 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 resistor.
- Ans. 4800 Ω.
Q. 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 other across the two wires of 220 V line if the maximum allowable current is 5 A ?
- Ans. 110.
Q.Which uses more energy :
(i) a 250 W T.V. set in 1 hour
(ii) a 1200 W toaster in 10 minutes ?