Consider a resistor of uniform cross-sectional area connected to a battery of internal resistance zero. If the length of the resistor is doubled by stretching it, then

 As the length is doubled, the cross-sectional area of the wire becomes half, thus the resistance of the wire $R=\rho L/A$  becomes four times the previous value. Hence after the wire is elongated, the current becomes one-fourth. Electric field is potential difference per unit length and hence becomes half the initial value. The power delivered to resistance is $P=V^2/R$ and hence becomes one-fourth.