Current flow through a transistor with no base current

In this relay kit, is there any current flow at all through the 2N3904 transistor when the transistor's base is set low by the Arduino pin?

Here is the datasheet for the 2N3904. I can't tell in there if there's any current flow at all.

http://www.mouser.com/ds/2/68/2n3903-29431.pdf

When the Arduino o/p goes low (0 Volts) there is no base current.
With no base current there is no collector current.

Thanks LarryD. I bet you know where I'm going with this. I think I'll take your suggestion to just use a small relay to turn off power to my H - Bridge to achieve a super low quiescent current. I can tell from all the things I've read in these forums and all the questions I've had answered that it can easily be done with a MOSFET but I'm just not comfortable enough with them yet to venture there.

use a small relay to turn off power

If the 5 volt relay coil (150 ohms or more) picks at 40mA or less you can use the Arduino o/p to drive the relay.
Don't forget to place a snubbing diode across the coil.
Good luck with your project.

Thanks. I'll post my schematic when completed.

Bear in mind that the relay coil current will add significantly to the battery drain when you do have the H-bridge powered up, even if the motor is not running.

Actually, with no base current, the collector current is dependent on the collector voltage and base impedance. And you really don't want to conduct any current under these conditions.

To be absolutely safe, the collector to emitter voltage needs to be kept less than BVceo, which for the 2N3904 is 40 V, so you are safe.