is the high utilization is because of traffic, and if yes then there could be a possibility of rise not because of broadcast but new addition of unicast reply from newly added users, in case application is two way.
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A well designed L2 switch should replicate broadcast packets in hardware, i.e. you shouldn't see much if any increase in the switch's CPU.
However, if the switch's management address is on the same subnet as the broadcasts, the switch's CPU might go high processing the received broadcasts.