As we are taking voltage as constant, the total power rating gets increased so the current also gets increased. The bulb filament may not bear that much current because it is rated to 60W.
As the blub filament is broken mechanically so one more thing the heater also does not work. Hence no current through the heater due to open circuit at the bulb.

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Power=V(square)/R...
So,for a constant voltage,the resistance value is finite
If voltage is 230Volts,R=5.29ohms...
Since already the bulb has an resistance,now since the heater and bulb connected in series the net resistance increases considerably and hence current is reduced only to an extent.
An hence bulb glows slightly dimmer but no major effect on bulb due to 10000W heater

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If voltage is 220V than current rating of bulb = 60/220 = 0.272amp (from ohm`s law) and resistance of bulb = 220*220/60 = 806.6 ohm.
For heater current = 1000/220 = 4.54 amp
and resistance = 220*220/1000 = 48.4 ohm
If both are connected in series on same voltage,
I mean 220 volts then
Total load = 806.6+48.4 =855 ohm.
Circuit current = 220/855 = 0.257 amp
Here circuit current is less than bulb rating so if both are connected in series than bulb will glow with dim light but heater
will not heat up.
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The bulb will get burnt only when there is more current flowing into it than rated current. Addition of another resistance in series will lead to addition of resistances and hence should result in a drop in the voltage across either one of them, ie less than rated voltage. So either will not do their function. The bulb wont light, the heater wont heat
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@ om_zzz
You are right, bulb will glow but dimmer and heater will not heat-up(more precisely it will generate very less heat)
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1 Thing everybody has to remember is that only current and not the voltage remains constant across the elements.Let us assume that the elements in series are connected to 220V supply source.
Total power to be supplied is 1000+60=1060W.
VI=1060..therfore current is 4.8A.This is the current that is flowing across both the elements.(heater as well as bulb).I^2/R=1000...resistance of heater=43.4ohms.Similarly resistance of bulb is 2.6ohms.
voltage across heater=208.32V
voltage across bulb=11.68V
So if the voltage rating of both the elements are 220V,bulb will be glowing very dim and heater would not work as expected!!!
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