Question

Timmy is playing with a new electonics kit he has recieved for his birthday. He takes out four resistors with resistances of 15ohms, 20ohms, 20ohms, and 30ohms. a) How would Timmy have to wire the risistors so that they would allow the maximum amount of current to be drawn? Calculate the total resistance in this circuit. b) How must he wire the resistors so that they draw a minimum amount of current? Calculate the total resisance in this circuit.

Answer 1

It's known that smallest resistance we can reach when using parallel connection, as on the circuit below.

Using parallel connection rule:

$$\frac {1}{R} = \frac {1}{R _ {1}} + \frac {1}{R _ {2}} + \frac {1}{R _ {3}} + \frac {1}{R _ {4}}$$ $$\frac {1}{R} = \frac {1}{1 5} + \frac {1}{2 0} + \frac {1}{2 0} + \frac {1}{3 0} = \frac {4 + 6 + 2}{6 0} = \frac {1 2}{6 0} = \frac {1}{5} \left(\frac {1}{\Omega}\right)$$

So,

$$R = 5 \Omega$$

It's known that smallest resistance we can reach when using series connection, as on the circuit below.

Using series connection rule:

$$R = R _ {1} + R _ {2} + R _ {3} + R _ {4}$$ $$R = 1 5 + 2 0 + 2 0 + 3 0 = 8 5 (\Omega)$$