The electrochemical cell stops working after some time because

Initially, the electrode potential of the cathode is not equal to the anode. Due to this, a potential gradient is developed. Electron transfer occurs from anode to cathode till the potential difference becomes equal. When potential difference between the cathode and anode is equal after sometime, the electron transfer is stopped. Hence, electrochemical cell stops working after some time because electrode potentials of both the electrodes become equal. Thus, the correct option is (b).