Resistance?

`1.) In this problem, you will calculate the basic quantities in a simple electric circuit. A 83 Ω resistor and a length of wire of resistance 18 Ω are connected in series across a 57 V power supply. Calculate the current flowing in the circuit. Give your answer in Amps 2.) Calculate the power dissipated in the 83 Ω resistor.. Give the answer in Watts.

Feb 16, 2018

1.) $I = 0.56 \text{ A}$

2.) $P = 26.4 \text{ W}$

Explanation:

The total resistance of the circuit is:

${R}_{\text{total" = 83" "Omega+18" }} \Omega$

${R}_{\text{total" = 101" }} \Omega$

The current in the circuit is the source voltage divided by the total resistance:

$I = \frac{V}{R} _ \text{total}$

$I = \left(57 \text{ V")/(101" } \Omega\right)$

$I = 0.564 \text{ A}$

The power dissipated by the resistor is the square of the current through it multiplied by the resistance of the resistor:

$P = {I}^{2} R$

$P = \left(0.564 \text{ A")^2(83" } \Omega\right)$

$P = 26.4 \text{ W}$