In the circuit shown ,when the switch is closed,the capacitor charges with time constant???

first close the switch and draw the circut. for RC circuit, the time constant is 

T= R_eq C

where R_eq is the effective resistance seen across the capacitor terminals with all independent sources making zero means voltage source value should be zero(short circuit)  and current source value should be infinity (open circuit) 

so now open the capacitor and short the voltage source and determine the resistance coming across the capacitor terminals.

one R is in parallel with short circuit. it will become zero resistance.

so R_eq = R

so T= RC