The invention claimed is:1. A switching circuit apparatus connected to first and second DC voltage sources, the switching circuit apparatus comprising:a first terminal to which a first voltage is applied from the first DC voltage source;a second terminal to which a second voltage lower than the first voltage is applied from the first DC voltage source;first and second switching elements connected in series between the first and second terminals, the first and second switching elements being connected via a first node;first and second drive circuits configured to control the first and second switching elements, respectively, to synchronously turn on and off;a first capacitor connected to the first node, the first capacitor applying a power supply voltage for the first drive circuit to the first drive circuit;a second capacitor connected to a negative electrode of the second DC voltage source and to the second terminal, the second capacitor applying a power supply voltage for the second drive circuit to the second drive circuit;a first diode connected between a positive electrode of the second DC voltage source and the first capacitor such that a current flows from the second DC voltage source to the first capacitor;a second diode connected between the positive electrode of the second DC voltage source and the second capacitor such that a current flows from the second DC voltage source to the second capacitor;a first series circuit including a first resistor and a first Zener diode connected in series between the first terminal and the first node, the first resistor and the first Zener diode being connected via a second node, the first resistor and the first Zener diode being connected in parallel with the first switching element, the first series circuit being connected such that a reverse bias voltage is applied from the first terminal to the first Zener diode via the first resistor; anda third diode connected between the second node and the first capacitor such that a current flows from the second node to the first capacitor.2. The switching circuit apparatus as claimed in claim 1, further comprising:a second series circuit including a second resistor and a second Zener diode connected in series between the first node and the second terminal, the second resistor and the second Zener diode being connected via a third node, the second resistor and the second Zener diode being connected in parallel with the second switching element, the second series circuit being connected such that a reverse bias voltage is applied from the first node to the second Zener diode via the second resistor; anda fourth diode connected between the third node and the second capacitor such that a current flows from the third node to the second capacitor.3. The switching circuit apparatus as claimed in claim 1, further comprising:a third resistor connected between the first drive circuit and the first switching element; anda fourth resistor connected between the second drive circuit and the second switching element.4. The switching circuit apparatus as claimed in claim 1, further comprisinga fifth resistor connected between the positive electrode of the second DC voltage source and the first capacitor; the fifth resistor being connected in series with the first diode.5. The switching circuit apparatus as claimed in claim 1, further comprisingthird and fourth Zener diodes connected in parallel with the first and second capacitors, respectively.6. A power converter apparatus comprising:at least one switching circuit apparatus; anda control circuit configured to control the at least one switching circuit apparatus,wherein the switching circuit apparatus is connected to first and second DC voltage sources, the switching circuit apparatus comprising:a first terminal to which a first voltage is applied from the first DC voltage source;a second terminal to which a second voltage lower than the first voltage is applied from the first DC voltage source;first and second switching elements connected in series between the first and second terminals, the first and second switching elements being connected via a first node;first and second drive circuits configured to control the first and second switching elements, respectively, to synchronously turn on and off;a first capacitor connected to the first node, the first capacitor applying a power supply voltage for the first drive circuit to the first drive circuit;a second capacitor connected to a negative electrode of the second DC voltage source and to the second terminal, the second capacitor applying a power supply voltage for the second drive circuit to the second drive circuit;a first diode connected between a positive electrode of the second DC voltage source and the first capacitor such that a current flows from the second DC voltage source to the first capacitor;a second diode connected between the positive electrode of the second DC voltage source and the second capacitor such that a current flows from the second DC voltage source to the second capacitor;a first series circuit including a first resistor and a first Zener diode connected in series between the first terminal and the first node, the first resistor and the first Zener diode being connected via a second node, the first resistor and the first Zener diode being connected in parallel with the first switching element, the first series circuit being connected such that a reverse bias voltage is applied from the first terminal to the first Zener diode via the first resistor; anda third diode connected between the second node and the first capacitor such that a current flows from the second node to the first capacitor.