# How can I calculate the equivalent resistance of this circuit?

## Homework Statement:

calculate the equivalent resistance of this circuit

## Relevant Equations:

...
i was trying to calculate equivalent resistance of this circuit

and that was my attempt :
1) i can see two parallel 20 ohm resistors so equivalent resistance = $${20 \over 2} = 10 ohm$$

2) now we are left with 20 ohm resistor and 10 ohm resistor which are connected in series so
equivalent resistance = $$20 + 10 = 30 ohm$$

the textbook tottaly ignores the resistor in the middle so the answer simply becomes $${20 \over 2} = 10 ohm$$ which does not make any sense to me , why should i ignore the resistor in the middle ? and when should i ignore a resistor ?

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kuruman
Homework Helper
Gold Member
This circuit shows that the battery is shorted. If you start at the positive terminal of the battery and you follow the circuit along the bottom branch after the junction on the left, you will reach the negative terminal of the battery without encountering any circuit element. Are you sure you reproduced the diagram correctly?

• archaic and DaveE
kuruman but if follow the electric current starting at postive terminal , electric current will flow in both top and bottom branches after the junction right ?

berkeman
Mentor
kuruman but if follow the electric current starting at postive terminal , electric current will flow in both top and bottom branches after the junction right ?
The current will divide in inverse proportion to the resistance of each branch. So the bottom shorted branch will take all of the current, and the top resistive branch will get no current as drawn.

More likely the original circuit had the middle resistor returning to someplace else, not to a shorted branch. Unless it's a trick question by a sinister professor... Something more like this would be a reasonable load circuit for such a question:

https://cdn.kastatic.org/ka-perseus-images/8305a10000c6f4066b2a4a46d353b1a5c0cc2ef6.svg As kuruman noted, the battery is short-circuited. @berkeman @kuruman
will the circuit still be shorted if the circuit looks something like this ?

kuruman
Homework Helper
Gold Member
@berkeman @kuruman
will the circuit still be shorted if the circuit looks something like this ?
Nope. That's known as a Wheatstone bridge. Can you figure this out? Hint: What could the potential difference across the 20 ohm resistor be?

Nope. That's known as a Wheatstone bridge. Can you figure this out? Hint: What could the potential difference across the 20 ohm resistor be?
potential difference will be the same across the 20 ohm resistor i guess ?

kuruman
Homework Helper
Gold Member
potential difference will be the same across the 20 ohm resistor i guess ?
The potential difference will be the same as what? Don't guess, reason it out.

• jbriggs444 and berkeman
scottdave