Find all currentsI1 I2 and ID and voltages across each compo

Find all currents(I_1, I_2 and I_D) and voltages across each component (V_R1, V_R2 and V_D) in the circuit shown below.

Solution

Here two voltages is applied via two resistor R1 and R2 across the capacitor. V1 is 10 V and V2 is 20V . as per the diagram, the anode of the diode is more negative with respect to cathode, so diode will remain off condition. No, current will flow through this. Hence diode current Id= 0 A.

In this condition R1 and R2 will be in series and these two resistor will be powered by two batteries. Again these two batteries are connected in additive mode. So, the total supply voltage in the modified circuit will be (10V+20V)= 30 V .

So, total current in this condition will be I= 30/(R1+R2)= 30/20= 1.5mA

again R1 and R2 is in series when diode is off, hence

IR1= 1.5 mA, IR2= 1.5mA and voltage drop across Resistor R1 is

VR1= 1.5mA x 10kOhm= 15 V and VR2= 1.5 mA x 10k ohm = 15 V

Id=0 mA

IR1=1.5mA

IR2=1.5mA

VR1= 15 V

VR2=15V

Voltage across the off diode (VD)will be

if we apply KVL at the left hand side loop then,

10-VR1-VD= 0

VD= -5V

or applying KVL at the right hand side of the loop,

+VD-VR2+20=0

VD=-5V

so, VD= -5V