Appending individual text file chars to string in C via strcat()

Question

I am trying to read in a text file char by char and append each char to a string.

This code here outputs what I expect, showing each individual char:

        char currentStr[MAX_WORD_LEN] = ""; 
        char cStrConvert[1] = "";
        char c;
        while((c = fgetc(filePtr)) != EOF)
        {
            cStrConvert[0] = c;
            printf("\ncStrConvert:%s\n", cStrConvert);
            //strcat(currentStr, cStrConvert);
            printf("\ncurrentStr: %s\n", currentStr);
        }

This is the output of the above:

cStrConvert:w

currentStr: 

cStrConvert:o

currentStr: 

cStrConvert:w //and so on for all the chars in the text file

However, when I make an attempt to append these chars to a string via strcat(); the code below,

        char currentStr[MAX_WORD_LEN] = ""; 
        char cStrConvert[1] = "";
        char c;
        while((c = fgetc(filePtr)) != EOF)
        {
            cStrConvert[0] = c;
            printf("\ncStrConvert:%s\n", cStrConvert);
            strcat(currentStr, cStrConvert);//try to append to the string
            printf("\ncurrentStr: %s\n", currentStr);
        }

cStrConvert:w

currentStr: w

cStrConvert:ow

currentStr: wow

cStrConvert:wwow

currentStr: wowwwoww

I have distilled this behavior to the one line that changes between the two code blocks, however I have no clue as to why it is not just appending each char to the currentStr. Additionally, strcat() seems to be changing cStrConvert as well.

Edit 2: Solution

I changed my definition of

char cStrConvert[1] = "";

to

char cStrConvert[2] = "";

to account for, and to be able to hold the null terminator character