A student designing an electrochemical method to recover copper from a recycling solution uses the standard reduction half-reaction

\[ \text{Cu}^{2+}\text{(aq)}+2e^-\rightarrow\text{Cu(s)} \qquad E^\circ=+0.34\ \text{V} \]

To combine the half-reaction with another half-reaction, the student multiplies all its coefficients by \(2\).

\[ 2\text{Cu}^{2+}\text{(aq)}+4e^-\rightarrow2\text{Cu(s)} \]

Which statement correctly gives the value of \(E^\circ\) for the multiplied half-reaction and explains why?