Question

The resistors in the circuit shown in Figure 19.2 each have a resistance of 700Ω. What Is the equivalent resistance of the circuit?

a. 2,800Ω

b. 1,400Ω

c. 700Ω

d. 175Ω

Answer 1

The equivalent resistance of the circuit, given that each resistor have a resistance of 700Ω, is 700Ω (option C)

How to calculate the equivalent resistance of the circuit?

First, we shall determine the equivalence of each parallel connection in the circuit. This is shown below:

For parallel connection 1:

• Resistor 1 (R₁) = 700 Ω
• Resistor 2 (R₂) = 700 Ω
• Equivalent resistance 1 (Rₑ₁) = ?

`R_(e1) = (R_1\ *\ R_2)/(R_1\ +\ R_2) \\\\R_(e1) = (700\ *\ 700)/(700\ +\ 700)\\\\R_(e1) = 350\ \Omega`

For parallel connection 2:

• Resistor 1 (R₁) = 700 Ω
• Resistor 2 (R₂) = 700 Ω
• Equivalent resistance 2 (Rₑ₂) = ?

`R_(e2) = (R_1\ *\ R_2)/(R_1\ +\ R_2) \\\\R_(e2) = (700\ *\ 700)/(700\ +\ 700)\\\\R_(e2) = 350\ \Omega`

Finally, we shall obtain the equivalent resistance in the circuit. This is shown below:

• Equivalent resistance 1 (Rₑ₁) = 350 Ω
• Equivalent resistance 2 (Rₑ₂) = 350 Ω
• Equivalent resistance of circuit (R) =?

`R = R_(e1)\ +\ R_(e2)`

= 350 + 350

= 700 Ω

Thus, the correct answer is option C