Consider all possible values of R in circuit shown. Then the maximum possible rate at which energy can be supplied by the ideal battery to the given combination of resistors is equal to

So here we want power delivered by battery should be maximumPower delivered by battery (V) to a resistance (R)P=V2RSo, for a given battery if R is minimum then P is maximumSo, hereIf R = 0 then equivalent resistance of circuit is minimum so 10 ΩIt would be short circuited So equivalent resistance of circuitReq=20ΩP=(20)2(20)=20W