Question

Determine the total resistance in a circuit containing one 25Ω

and one 15Ω resistor.
To be honest, I don't understand this at all.

Answer 1

9.375 Ω

Explanation:

You want the resistance that is equivalent to parallel resistors of 25Ω and 15Ω.

Parallel resistors

The formula for the equivalent resistance of resistors in parallel is ...

`R_(eq)=(1)/((1)/(R_1)+(1)/(R_2)+(1)/(R_3)+\dots+(1)/(R_n))`

For the given circuit, we have ...

`R_1=25\Omega,R_2=15\Omega\\\\R_(eq)=(1)/((1)/(25)+(1)/(15))=(1)/((3+5)/(75))=(75)/(8)=9.375\quad\text{ohms}`

The total resistance of the circuit is 9.375Ω.

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Additional comment

The current through the fuse is the sum of the currents through the parallel branches of the circuit: I₁ + I₂. For some source voltage E, the sum of those currents is ...

I₁ + I₂ = E/R₁ + E/R₂

The equivalent resistance is the resistance that gives that same current for that same voltage:

`R_(eq)=(E)/(I_1+I_2)=(E)/((E)/(R_1)+(E)/(R_2))=(R_1R_2)/(R_1+R_2)\\\\\\=(25\cdot15)/(25+15)=(375)/(40)=9.375\quad\text{ohms}`