Question

Refer to Ohm's Law given in the previous question.

If the voltage in a circuit is 35+j12 volts and the resistance is 2+j4 ohms, what is the current?

A) −596+j293 amps
B) −196+j293 amps
C) 33−j8 amps
D) 5910−j295 amps
E) 37+j16 amps
F) 118−j164 amps

Answer 1

To find the current in the circuit, use Ohm's Law to divide the voltage by the resistance. Apply the formula for complex number division to obtain the final result.

Step-by-step explanation:

To find the current in the circuit, we can use Ohm's Law which states that the current (I) is equal to the voltage (V) divided by the resistance (R), or I = V / R. In this case, the voltage is 35+j12 volts and the resistance is 2+j4 ohms. We can divide the complex numbers using the formula (a+jb) / (c+jd) = (ac+bd)/(c^2+d^2) + j(bc-ad)/(c^2+d^2), where a, b, c, and d are real numbers.

Applying the formula, we get:

I = (35 * 2 + 12 * 4) / (2^2 + 4^2) + j(12 * 2 - 35 * 4) / (2^2 + 4^2)

= (70 + 48j) / (4 + 16) + j(24 - 140) / (4 + 16)

= (70 + 48j) / 20 + j(-116) / 20

= 3.5 + 2.4j - 5.8j

= 3.5 - 3.4j

So, the current in the circuit is approximately 3.5 - 3.4j amps.

Answer 2

Ohm's Law: voltage = resistance times current. Here we know voltage and resistance, but must calculate the current.

current = voltage / resistance

35 + 12j

Here, current = --------------- amps

2(1+2j)

We must rationalize the denominator (remove 'j' from the denom.). To do this, multiply numerator and denominator of the above fraction by (1-2j), obtaining:

(25+12j)(1-2j) 25-50j+12j+24 49 - 36j

------------------- = ------------------------ = ---------------- ohms (answer)

2(1 + 4) 10 10