microcontroller Why this transistor logic as switch is not working

  
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I opened remote of a RC car and extended wires out of backward, forward, left and right switches. So when I ground anyone of then the circuit completes andit sends signal to the car. I wanted to close the circuit using one of the I/O pins of BeagleBone Black. The output voltage on these I/O pins is about 3. 3V. I found out that I can use transistor as a switch but after a putting all the things
microcontroller Why this transistor logic as switch is not working - schematic

together the circuit remains closed even without supplying base voltage to transistor as shown in the diagram. I am also showing the calculations used by me to get the resistances required at the Base terminal. Transistors can be used a switch when you supply base current. The circuit remains closed without supplying any base voltage. In short the collector emitter terminal are closing the circuit from one of the remote pins with ground. I wanted the circuit to close when I turn one of the pins on the BeagleBone high. I am doing something wrong but I don`t know what I am doing wrong. Any suggestions in the right direction would be greatly appreciated.



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