Current through a diode paralleled with a resistor

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I'm confused on a homework question in my intro to electrical systems class. I have a simple dc circuit with a voltage source of 4.7 volts in series with a 40 ohm resistor, that then connects to a 50 ohm resistor paralleled with a diode in series with a 20 ohm resistor that then connects back to the negative terminal of the voltage source. The problem is that I've calculated the current through the first resistor as 117.5 mA, and I'm trying to find the current through the diode, which after getting the question wrong the homework program tells me the answer is 45.3 mA. Yet that would mean the 50 ohm resistor has 72.2 mA flowing across, which is greater than the current flowing across the 20 ohm resistor.

Why is it that a paralleled resistor does not have more current flowing across the path with less resistance?

what affect does the diode have on current?

assuming the diode is ideal and has voltage drop of .6 V

Best Answer

KCL for the junction is $$I_1=I_2+I_3$$ The voltage on the junction is \$V_1\$ Then $$I_1=(4.7-V_1)/40$$ $$I_2=V_1/50$$ $$I_3 = (V_1-0.6)/20$$

Solving: $$ (4.7-V_1)/40 = V_1/50 + (V_1-0.6)/20 $$ giving us $$V_1=1.55V$$ Hence $$I_3=(1.55-0.6)/20=0.0475A=47.5mA$$ Close enough to \$45.3\$..`.