a circuit has a diode (whose potential drop across it is givn to be .5V and maximum power is 100mW). What should be the value of resistance connected in series with the diode. The emf of the cell attached is 1.5 V .

Voltage across the diode is 5 v.
power across the diode is given by : P = VI = 0.1 W
Current across the conductor is given by 
I = P/V = 0.1/5 = 0.02 A
As resistance is connected in series with the diode then same current will follow through the resistance .
Voltage cell = 1.5 volt
resistance = 1.5/0.02 = 75 Ω

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