Question 728: Current Electricity

Question

Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100, 60 and 40 W bulbs have filament resistances R
100
, R
60
and R
40
respectively, the relation between these resistances is

Accepted Answer

The power of the bulb is
$$P = {{{V^2}} \over R}$$
Therefore,
$$100 = {{{V^2}} \over {{R_{100}}}} \Rightarrow {1 \over {{R_{100}}}} = {{100} \over {{V^2}}}$$
where R
100
is the resistance (at any temperature) corresponds to 100 W. Similarly,
$$60 = {{{V^2}} \over {{R_{60}}}} \Rightarrow {1 \over {{R_{60}}}} = {{60} \over {{V^2}}}$$ and $$40 = {{{V^2}} \over {{R_{40}}}} \Rightarrow {1 \over {{R_{40}}}} = {{40} \over {{V^2}}}$$
From these equations, we get
$${P_{100}} > {P_{60}} > {P_{40}} \Rightarrow {1 \over {{R_{100}}}} > {1 \over {{R_{60}}}} > {1 \over {{R_{40}}}}$$

Answer

$${1 \over {{R_{100}}}} = {1 \over {{R_{40}}}} + {1 \over {{R_{60}}}}$$

Answer

$${R_{100}} = {R_{40}} + {R_{60}}$$

Answer

$${R_{100}} > {R_{60}} > {R_{40}}$$

Answer

$${1 \over {{R_{100}}}} > {1 \over {{R_{60}}}} > {1 \over {{R_{40}}}}$$

Current Electricity

Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100, 60 and 40 W bulbs have filament resistances R 100 , R 60 and R 40 respectively, the relation between these resistances is

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