Consider this circuit.Let R₁ = R₂ = R₃ = R₄ = R₅ = 10 $\varOmega$.If V= 20 V then what is the current I_V going through the circuit?

Question

Quizplus · Accepted Answer

Since all the capacitors have the same capacitance value, they will all experience the same voltage drop across them. Therefore, the voltage drop across C1, C2, C3, C4, and C5 will be 4 V each (20 V divided by 5). The resistors R1, R2, R3, R4, and R5 are all in series, so their total resistance is 5 Ω (1 Ω + 1 Ω + 1 Ω + 1 Ω + 1 Ω). Therefore, the current through the circuit is I = V/R = 20/5 = 4 A. Since the same current flows through each resistor, the voltage drop across each resistor will be proportional to its resistance. Therefore, the voltage drop across R1, R2, R3, R4, and R5 will be 0.8 V each (4 V multiplied by 1/5). The current through each capacitor will be given by I = C(dV/dt). Since the voltage across each capacitor does not change abruptly, we can assume that the current through each capacitor is constant. Therefore, the current through each capacitor will be I = 10 F (4 V/1 s) = 40 A/s. The voltage drop across each capacitor and resistor is shown in the following diagram: The current I_V is the same as the current through R5, so I_V = 0.8 V/1 Ω = 0.8 A. However, the question asks for the current in A, not in A/s, so we must convert the current through the capacitors to an equivalent current through the resistors. Since the capacitors have been charged to 4 V, the current through them will decrease exponentially as they discharge. Therefore, we must integrate the current over time to obtain the equivalent current through the resistors: Q = CV = 10 F x 4 V = 40 C I_equivalent = Q/t = 40 C/1 s = 40 A Therefore, the total current through the circuit is I_total = 0.8 A + 40 A = 40.8 A. However, we must be careful to convert the units to A: I = 40.8 A/s x 1 s/1000 s = 0.0408 A So the final answer is 0.0408 A, which is closest to 0.05 A or 1.0 A. The best choice is B), 1.0 A.

Consider This Circuit Ω\varOmegaΩ If V= 20 V Then What Is the Current IV

Consider This Circuit $\varOmega$ If V= 20 V Then What Is the Current I_V