Equivalently implementing a generalized memristor by using common components and then making a nonlinear circuit with a reliable property, are conducive to experimentally exhibit the nonlinear phenomena of the memristive chaotic circuit and show practical applications in generating chaotic signals. Firstly, based on a memristive diode bridge circuit, a new first-order actively generalized memristor emulator is constructed with no grounded restriction and ease to realize. The mathematical model of the emulator is established and its fingerprints are analyzed by the pinched hysteresis loops with different sinusoidal voltage stimuli. The results verified by experimental measurements indicate that the emulator uses only one operational amplifier and nine elementary electronic circuit elements and is an active voltage-controlled generalized memristor. Secondly, by parallelly connecting the proposed emulator to a capacitor and then linearly coupling with an RC bridge oscillator, a memristor based chaotic circuit without any inductance element is constructed. The dynamical model of the inductorless memristive chaotic circuit is established and the phase portraits of the chaotic attractor with typical circuit parameters are obtained numerically. The dissipativity, equilibrium points, and stabilities are derived, which indicate that in the phase space of the inductorless memristive chaotic circuit there exists a dissipative area where are distributed two unstable nonzero saddle-foci and a non-dissipative area containing an unstable origin saddle point. Furthermore, by utilizing the bifurcation diagram, Lyapunov exponent spectra, and phase portraits, the dynamical behaviors of the inductorless memristive chaotic circuit are investigated. Results show that with the evolution of the parameter value of the coupling resistor, the complex nonlinear phenomena of the coexisting bifurcation modes and coexisting attractors under two different initial conditions of the state variables can be found in the inductorless memristive chaotic circuit. Finally, a prototype circuit with the same circuit parameters for numerical simulations is developed, from which it can be seen that the prototype circuit has a simple circuit structure and is inexpensive and easy to practically fabricate with common components. Results of both the experimental measurements and the numerical simulations are consistent, verifying the validity of the theoretical analyses.