>For a constant load, how does increasing supply voltage increase speed of the motor?

- Speed ∝ voltage.
- Torque ∝ current.

Let's imagine the following:

- The motor is connected to the voltage source and is running at a constant speed. The back EMF has risen and the current has reduced from its starting value and is stable.
- If we now increase the voltage the current will increase. Remember that the current, \$ I = \frac {V_S - V_{bEMF}}{R} \$ where *R* is the motor resistance.
- The increased current will give increased torque which will accelerate the motor to its new steady speed.

>But we know that speed is inversely proportional to armature current.

No. Speed is proportional to voltage. If you try to stall a motor running on constant voltage you will see the current rise. However, given a constant voltage the current will decrease as you approach the speed for that voltage. That may be the source of your confusion.

You could get a good feel for this if you have access to a lab power-supply with a voltage and current meter along with a suitable DC motor. Try running the motor in constant voltage mode an in constant current mode.