Electricity Worksheet-25
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A wire 1.0 m long, 2.0 mm in diameter, has a resistance of 10 Ω. Calculate the resistivity of its material.
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Calculate the area of cross – section of a wire if its length is 1.0m, its resistance is 23 Ω and the resistivity of the material is 1.84 × 10–6 Ω m.
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Calculate the resistance of an electric bulb which allows a 10 A current when connected to a 220 V power source.
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A lamp rated 100 W at 220 V is connected to the mains electric supply. What current is drawn from the supply line if the voltage is 220 V ?
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Calculate the electric energy consumed by a 1200 W toaster in 20 minutes.
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A torch bulb is rated 5.0 V and 500 mA. Calculate its (i) power (ii) resistance and (iii) energy consumed when it is lighted for 4 hours.
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Two electric lamps of 100 W and 25 W respectively are joined in parallel to a supply of 200 V. Calculate the total current flowing through the circuit.
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Two identical resistors, each of resistance 2 Ω, are connected in turn (i) in series, and (ii) in parallel, to a battery of 12 V. Calculate the ratio of power consumed in the two cases.
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Two identical resistors, each of resistance 10 Ω are connected in (i) series, and (ii) in parallel, in turn to a battery of 10 V. Calculate the ratio of power consumed in the combination of resistors in the two cases.
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In the given circuit calculate (i) total resistance of the circuit, and (ii) current shown by the ammeter.
Answer:
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Her;
I = 1.0 m, R = 23 Ω, p = 1.84 × 10–6 Ωm
As
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I = 10A, V = 220 V. As V = IR,
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Here; P = 100 W, V = 220 V. As P = VI,
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P = 1200 W, t = 20 min = 20 × 60 s = 1200 s
Electric energy consumed, W = Pt = (1200 W) (1200 s) = (1200 J/s) (1200 s) = 1.44 × 106 J
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V = 5V, I = 500mA = 0.5A
(i) P = VI = 5C × 0.5 A = 2.5 W
(ii) R = V/I = 5V/0.5 A = 10 Ω
(iii) W = P × t = 2.5 W × 4 hour = 2.5 W × (4 × 3600s) = 3600 J
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When the lamps are joined in parallel, equivalent power,
P = P1 + P2 = 100 W + 25 W = 125 W
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(i) Total resistance in series, Rs = 2 Ω + 2 Ω = 4 Ω
Power consumed,
(ii) Total resistance in parallel, i.e., Rp is given by or Rp = 1 Ω
Power consumed in parallel,
or Ps : Pp = 1:4
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(i)
(ii)
or Ps : Pp = 1:4
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(i) Since R1 and R2 are in series, their resultant resistance,
Rs = R1 + R2 = 3 Ω = 3 Ω + 2 Ω = 5 Ω
Further, Rs and R3 are in parallel, their resultant is given by
or Rp = 25 Ω.
(ii)