Respuesta :
Answer:
The answer to the question is
The current through R4 = 0.5865 mA
Explanation:
To solve this we list out the known thus
Voltage source = 45-V
Firsrt parallel circiuit has resistances of R1 = 17 kΩ and R2 = 23 kΩ
Second parallel circiuit has resistances of R3 = 45 kΩ and R4 = 55 kΩ
we first find the current flowing in the circuit by finding thr sum of the total resistance in eah parallel circuit
Firsrt parallel circiuit, for circuit in parallel, sum of resistance 1/RT1 = 1/ R1 + 1/R2 = 1/17+1/23 = 0.1023017 therefore RT1 = 1/0.1023017 = 9.775 kΩ
Similarly we have for the second parallel circuit 1/RT2 = 1/R3 + 1/R4
= 1/45 + 1/55 = 0.0404 Hence RT2 = 1/0.0404 = 24.75 kΩ
This means that the 9.775 kΩ and the 24.75 kΩ are in series hence total resistance of the circuit = sum of all resistances in series
= 9.775 kΩ + 24.75 kΩ = 34.525 kΩ
However current, I is given by V/R = 45-V/34.525 kΩ = 1.303 × 10⁻³ A or 1.303 mA
From the current divider rule, I4 = I × (R4/(R3+R4)
That is the currrent flowing throuhgh R4 = 1.303 × (45/(45+55)) = 0.5865 mA
