COMPLETE QUESTION: 
<em>When the magnetic flux through a single loop of wire increases by </em>30 Tm^2<em> , an average current of 40 A is induced in the wire. Assuming that the wire has a resistance of </em><em>2.5 ohms </em><em>, (a) over what period of time did the flux increase? (b) If the current had been only 20 A, how long would the flux increase have taken?</em>
Answer:
(a). The time period is 0.3s.
(b). The time period is 0.6s. 
Explanation:
Faraday's law says that for one loop of wire the emf  is
 is 

and since from Ohm's law 
 ,
,
 then equation (1) becomes 

(a). 
We are told that the change in magnetic flux is  ,  the current induced is
,  the current induced is  , and the resistance of the wire is
, and the resistance of the wire is  ; therefore, equation (2) gives
; therefore, equation (2) gives 

which we solve for  to get:
 to get: 

 ,
,
which is the period of time over which the magnetic flux increased.
(b). 
Now, if the current had been  , then equation (2) would give
, then equation (2) would give



which is a longer time interval than what we got in part a, which is understandable because in part a the rate of change of flux  is greater than in part b, and therefore , the current in (a) is greater than in (b).
 is greater than in part b, and therefore , the current in (a) is greater than in (b).