I am using an Arduino Nano for a project along with a 16 x 2 LCD display (hoping to up that to 20 x 4). It has the I2C unit fitted and by putting my multimeter in series with the cable going to the VCC pin on the display, it was measuring about 14mA including backlight being on. I was thinking that was a bit low! Does that sound right?
Thanks
A common "1602" display has resistor "R8" at 100 Ohms (marked "101") resulting in a backlight current of about 24 mA. I presume when you refer to "in series with the cable going to the VCC pin on the display" that you mean pins 2 and 15. Did you add a resistor in series with pin 15, perhaps another 100 Ohm?
The current drawn from pin 2 is about 1.5 mA, so you would be measuring mostly the backlight. Incidentally, where is your circuit diagram and how have you connected pin 3?
Paul__B:
A common "1602" display has resistor "R8" at 100 Ohms (marked "101") resulting in a backlight current of about 24 mA. I presume when you refer to "in series with the cable going to the VCC pin on the display" that you mean pins 2 and 15. Did you add a resistor in series with pin 15, perhaps another 100 Ohm?The current drawn from pin 2 is about 1.5 mA, so you would be measuring mostly the backlight. Incidentally, where is your circuit diagram and how have you connected pin 3?
Many thanks for the reply. The I2C module is soldered on to the LCD display and the connections are VCC(I2C) to 5V(Nano), GND(I2C) to GND(Nano), SDA(I2C) to A4(Nano) and SCL(I2C) to A5(Nano) no additional resistors and there is no jumper on the I2C to add a resistor to. I presumed that if I measured the current being drawn from the 5V pin that that would be the total current drawn by the LCD, which as I say is 14mA. I may be doing something wrong but I don't think so.
OK, I didn't originally notice that you had the backpack fitted. Silly me! 
The backpack includes a transistor to switch the backlight, this may be dropping the voltage slightly and consequently reducing the current. If the backlight is on and the display is operating properly then there is nothing to worry about. You might just check the actual voltage being delivered to the display on pins 2 and 15. If you are operating from a USB supply it is often significantly below 5 V and there is indeed a diode in series with the USB input on the Nano so you may be getting only 4.4 V. 
Paul__B:
OK, I didn't originally notice that you had the backpack fitted. Silly me!The backpack includes a transistor to switch the backlight, this may be dropping the voltage slightly and consequently reducing the current. If the backlight is on and the display is operating properly then there is nothing to worry about. You might just check the actual voltage being delivered to the display on pins 2 and 15. If you are operating from a USB supply it is often significantly below 5 V and there is indeed a diode in series with the USB input on the Nano so you may be getting only 4.4 V.
I'll check the voltage but it appears to be operating as it should. Your assistance is much appreciated.
Thanks