smaller earphones, and especially ones with less efficient drivers have high Impedance ratings; the higher the impedance the lower the current (ohm’s law), so check the impedance rating on your earphones; generally 16 Ohms is the standard rating, but lower output earphones (i.e. Those with lower sound output have higher impedance ratings like 32 Ohms.
Not taking voltage into account the general rule of thumb in audio electronics is the lower the impedance the higher the current draw (and higher the power consumption). Many studio grade headphones with the larger drivers are rated at 8 Ohms, and thusly draw a larger current, but as chaosrob mentioned there is a max power output (measured in milliwatts or mW) that is an expression based on power consumption (voltage times current).
Wiki Ohm’s Law for a more in-depth explanation of electrical circuits and power consumption.