A rheostat is connected in series to the arc lamp, the resistance of which is 5 Ohm.

| September 6, 2021 | education

A rheostat is connected in series to the arc lamp, the resistance of which is 5 Ohm. Determine the current in the lamp if the voltage at the generator terminals is 127 V. The wiring is made with copper wire. The length of the wire is 20 m and its cross-sectional area is 18 mm2. The restat is fully switched on and its resistance is 7.5 Ohm.

Let us find the resistance of the wire Rp, if the length of the wire l is 20 m, the cross-section of the wire S is 18 mm², the resistivity of copper p is 1.7 / 10⁸:
Rp = p * l / S = 1.7 * 20 * 10⁶ / 18 * 10⁸ = 1.9 / 100 = 0.02 Ohm.
Let’s find the total resistance of the circuit Ro, if the resistance of the arc lamp is 5 Ohm, the resistance of the rheostat is 7.5 Ohm:
Ro = 7.5 + 5 + 0.02 = 12.52 Ohm.
Find the circuit current if the circuit voltage is 127 V:
I = 127 / 12.52 = 10.14 A.
Answer: the current flowing through the circuit is 10.14 A.



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