How does C have effects on bias and variance of a Support Vector Machine?
The C being a regularized parameter, controls how much you want to punish your model for each misclassified point for a given curve.
If you put large value to C it will try to reduce errors but at the same time it may happen that it would not perform better on test dataset hence cause overfitting.
To get to know more about effect of C in svm. Refer this.