In the autoregressive model AR(p). Why $\mathbb{E}[X_{t}Z_{t}] =\operatorname{Var}[Z_{t}] $?

Question

In the Autoregressive model AR(p), of time series, where $X_t=\sum_{i=1}^{p}\phi_{i}X_{t-i}+ Z_{t}$ (Where $Z_t$ is the white noise, $\phi_k$ are constants and $X_t$ random variables) Why is that expected value equal to the variance of $Z_{t}$? Is it related to the fact that we can write the model as a MA($\infty$)? I think that this is obvious because I can't find the explanation. Sorry for asking but I can't stop thinking about it