Complex numbers are used in electronics to describe the current in an electric circuit. Ohm's law relates the current in a circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the circuit, R, in ohms, by the formula E - IR. Solve the problem using this formula. Find E, the voltage of a circuit, if I (16 + ) amperes and R=2+4) ohms (32 + 66i volte.

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Mathematics

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27 June, 16:52

Complex numbers are used in electronics to describe the current in an electric circuit. Ohm's law relates the current in a circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the circuit, R, in ohms, by the formula E - IR. Solve the problem using this formula. Find E, the voltage of a circuit, if I (16 + ) amperes and R=2+4) ohms (32 + 66i volte.

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Isai Calderon · Answer 1

E = 3072i - 5904ohms

Step-by-step explanation:

From ohms law recalled that E = IR given already

E = voltage (volts)

I = Current (amps)

R = resistance (ohms)

Therefore, by substitution

I = 16i and R = (2+4) ohms (32+66i)

= 6 (32+66i) ohms

= (192+396i) ohms

E = (16i) * (192+396i)

E = 3072i + 5904i²

Recall that i² = - 1 from complex number

E = 3072i + 5904 (-1)

E = 3072i - 5904ohms