A one-meter wire segment has a total resistance of 560 . (a) If a battery is att

Question

A one-meter wire segment has a total resistance of 560 . (a) If a battery is attached to the wire with a potential difference of 70 Volts, what current flows through the wire? (b) Four of these wire segments are attached end-to-end and hooked up to the same battery. What new current flows through the wire? (Hint: think of each wire segment as a resistor!) (c) Several wire segments are attached in series to form a long wire. How long is the wire (constructed from identical wire segments) if the current flowing through it is 7.8 mA?

Explanation / Answer

Given :

Length of wire = l = 1m

resistance of the wire = R = 560 ohm

Potential difference = V = 70 volts

a. current flowing through the wire = i = V/R= 70/560= 0.125 A ( applying ohm's law)

b. four wires are attached end-to-end i.e. resistors are connected in parallel.

If four resistors of resistance R are connected in parallel, then effective resistance = R/4

in this case, the new resistance of 4 wires = 560/4 = 140 ohm

Now, current flowing through the wire = i = V/R= 70/140= 0.5 A ( applying ohm's law)

c. several wire segments are attached in series to form a long wire.

let us assume that n no of wires are attached.

then effective resistance of n wires of resistance R each attached in series = nR

in this case the effective resistance of n wires of resistance 560 ohm each attached in series= n x 560

as current = voltage / resistance = 70/ (n x 560) = 7.8 x 10 -3

so, n= 70/(560 x7.8 x 10-3)

= 16

As length of each wire is 1m, the total length of wire = 16 x 1 = 16 m

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