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A voltmeter has a resistance of G ohm and range V volts. The value of resistance used in series to convert it into a voltmeter of range nV volts is :

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Explanation

We know that;

R=VIg-G

The voltmeter gives the full-scale deflection for potential difference V. Its resistance is G.

Hence,

Ig=VG

Given that V = nV. Therefore,

R=nV(V/G)-G=(n-1)G

An ammeter is obtained by shunting a 30 Ω galvanometer with a 30 Ω resistance. What additional shunt should be connected across it to double the range?

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Explanation

The total range is doubled, i.e., 4Ig.

Now shunt required is :

 S=Ig4Ig-Ig×G=10 ΩThis is the resultant shunt.So,130+1x=110 or x=15 Ω

Two similar headlight lamps are connected in parallel to each other. Together, they consume 48 W from a 6 V battery. What is the resistance of each filament?

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Explanation

The power consumed by each lamp is 24 W.

Hence, using R = (V2/P), we find R = (36/24) = 1.5 Ω.

Two electric bulbs, rated for the same voltage, have powers of 200 W and 100 W, respectively. If their resistances are r1 and r2, respectively then :

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Explanation

P=V2R, P1P2=R2R1 or r2=2r1

If the current in an electric bulb decreases by 0.5%, the power in the bulb decreases by approximately :

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Explanation

P=i2R, dPP=2dII=2×0.5%=1%

An electric bulb rated for 500 W at 100 V is used in a circuit having a 200 V supply. The resistance R that must be put in series with the bulb, so that the bulb draws 500 W, is :

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A wire, when connected to a 220 V mains supply, has power dissipation P1. Now, the wire is cut into two equal pieces, which are connected in parallel to the same supply. Power dissipation in this case is P2. Then P2:P1  is :

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Explanation

P=V2/R.

R is reduced by a factor of 4.

So, P is increased by a factor of 4.

The resistance of hot tungsten filament is about 10 times the cold resistance. What will be the resistance of 100 W and 200 V lamp when not in use?

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Explanation

When the filament is hot, R=V2P=200×200100=400 Ω

Hence, when cold, the resistance is 40 Ω.

Two electric bulbs A and B are rated 60 W and 100 W, respectively. If they are connected in parallel to the same source, then,

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Explanation

Given PA=60 W, PB=100 W. We know that current flowing through the bulb is I = P/V. We also know that as both the bulbs are connected in parallel, potential difference (V) across both the bulbs is the same. Thus, I α P. Since the power of bulb B is greater than that of bulb A, bulb B draws more current than bulb A.

A factory is served by a 220 V supply line. In a circuit protected  by a fuse marked 10 A, the maximum number of 100 W lamps in parallel that can be turned on is :

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Explanation

The current required by each bulb is :

I=PV=100220A

If n bulbs are joined in parallel, then,

nI=Ifuse or n×100220=10 or n=22.

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