Solve each problem. Be sure to show your work and give a final answer with units rounded to the given number of significant figures.
1) Find the voltage on a circuit with a resistance of 12.5 Ω if it has a current of 2.35 A.
2) If a circuit with a 9.0 V battery has a current of 6.2 A, how much resistance is in the circuit?
3) A circuit has three resistors with values of 4.0 Ω, 8.0 Ω, and 12 Ω. What is the equivalent resistance if they are wired in series?
4) A circuit has three resistors with values of 4.0 Ω, 8.0 Ω, and 12 Ω. What is the equivalent resistance if they are wired in parallel?
1. V = i R
2. so R = V/i
3. resistors in series add, same current through each so the iR voltages add
4. In parallel, the currents add for the same voltage on each
so i1 = V/R1 and i2 = V/R2 and i3 = V/R3
so
i = i1 + i2 + i3 = V(1/R1+1/R2+1/R3)
but overall, i = V/Req where Req is the equivalent resistance we want
so
V/Req = V(1/R1+1/R2+1/R3)
Req = 1 / (1/R1 + 1/R2 + 1/R3)
https://www.electronics-tutorials.ws/resistor/res_4.html
Oh, I get. Thank sm, Damon! :)
To solve these problems, we will use the following formulas:
1) Ohm's Law: V = I * R, where V is the voltage, I is the current, and R is the resistance.
2) Ohm's Law: V = I * R, but in this case, we need to solve for R.
3) The formula for the equivalent resistance of resistors wired in series is: Req = R1 + R2 + R3 + ...
4) The formula for the equivalent resistance of resistors wired in parallel is: 1/Req = 1/R1 + 1/R2 + 1/R3 + ...
Let's solve each problem step-by-step:
1) Given: R = 12.5 Ω, I = 2.35 A
Using Ohm's Law: V = I * R
V = 2.35 A * 12.5 Ω
V = 29.375 V
Rounding to the correct number of significant figures gives the final answer: V = 29 V
2) Given: V = 9.0 V, I = 6.2 A
Using Ohm's Law: V = I * R
9.0 V = 6.2 A * R
R = 9.0 V / 6.2 A
R = 1.45 Ω
Rounding to the correct number of significant figures gives the final answer: R = 1.5 Ω
3) Given: R1 = 4.0 Ω, R2 = 8.0 Ω, R3 = 12 Ω
Using the formula for resistors in series: Req = R1 + R2 + R3
Req = 4.0 Ω + 8.0 Ω + 12 Ω
Req = 24 Ω
Rounding to the correct number of significant figures gives the final answer: Req = 24 Ω
4) Given: R1 = 4.0 Ω, R2 = 8.0 Ω, R3 = 12 Ω
Using the formula for resistors in parallel: 1/Req = 1/R1 + 1/R2 + 1/R3
1/Req = 1/4.0 Ω + 1/8.0 Ω + 1/12 Ω
1/Req = 0.25 Ω⁻¹ + 0.125 Ω⁻¹ + 0.0833 Ω⁻¹
1/Req = 0.4583 Ω⁻¹
Req = 1 / 0.4583 Ω
Req ≈ 2.180 Ω
Rounding to the correct number of significant figures gives the final answer: Req = 2.2 Ω