This circuit converts a current at its input to a voltage at its output. It is typically used for digital signals, and with a base resistor at the first transistor. (In that case, if the base resistor is larger than R_L, the output impedance is lower than the input impedance, i.e., the circuit amplifies the current.)

U_e and U_a,2 are not actually interesting, because both transistors are either off or saturated.

The capacitor slows down switching on the second transistor. This might be useful if you want to balance the switching times (a saturated transistor is slower switching off than switching on). For example, such a capacitor is used in the Roland MKS-30 to ensure that the falling and raising edges of the MIDI signal are delayed by approximately the same amount:

This circuit converts a current at its input to a voltage at its output. It is typically used for digital signals, and with a base resistor at the first transistor. (In that case, if the base resistor is larger than R_L, the output impedance is lower than the input impedance, i.e., the circuit amplifies the current.)

U_e and U_a,2 are not actually interesting, because both transistors are either off or saturated.

The capacitor, if it has been put there deliberately and does not just represent a parasitic capacitance, slows down switching on the second transistor. This might be useful if you want to balance the switching times (a saturated transistor is slower switching off than switching on). For example, such a capacitor is used in several Roland MIDI devices to ensure that the falling and raising edges of the MIDI signal are delayed by approximately the same amount: