Charging of resistor with resistance in parallel

[AdityaDev]

The cell can provide conatant emf ε and initial charge of capacitor is zero.
Now current through resistor initially is zero and increases. But the potential difference across the capacitor is always a constant with magnitude ε.
then $\frac{q(t)}{C}=E$
So $q(t)=CE$ which implies q is constant and non zero. So initial charge in capacitor can never be zero! But this contradicts the initial condition. What mistake am I doing? I am trying to find the time constant.

 

[phinds]

The cell can provide conatant emf ε and initial charge of capacitor is zero.
Now current through resistor initially is zero and increases. But the potential difference across the capacitor is always a constant with magnitude ε.
then $\frac{q(t)}{C}=E$
So $q(t)=CE$ which implies q is constant and non zero. So initial charge in capacitor can never be zero! But this contradicts the initial condition. What mistake am I doing? I am trying to find the time constant.

The problem with ideal things is that they can lead to unphysical situations such as this. An idea capacitor does start off with zero volts and an ideal voltage source provides that voltage as soon as it comes on and continues to provide it, unwaveringly. This leads to the situation here where the initial current is infinite, which is unphysical.

 

[AdityaDev]

So the time constant for charging of capacitor is zero.

 

[phinds]

So the time constant for charging of capacitor is zero.

Again, this is an unphysical situation. I'm an engineer. As far as I'm concerned, the answer is irrelevant because it is impossible. Real world power sources and wires to capacitors have resistance, even if only a small amount.