The model of an electric circuit with dichotomous resistance is investigated. It is shown that the dichotomous resistance can induce a phenomenon of stochastic giant resonance for the signal-to-noise ratio (SNR) as a function of input signal frequency. This phenomenon is a direct consequence of the existence of a zero noise power spectrum, with a nonzero signal power spectrum for the same parameters. In addition, two kinds of the usual stochastic resonance phenomena have been obtained for the SNR. One is as a function of the correlation time of the asymmetric dichotomous resistance; the other is as a function of the input signal frequency.