A 10 m long uniform metallic wire having a resistance of `20 Omega` is used as a potentiometer wire. This wire is connected in series with another resistance of `480 Omega` and a battery of emf 5 V having negligible internal resistance. If an unknown emf e is balanced across 6 m of the potentiometer wire, calculate :
the potential gradient across the potentiometer wire.

Explanation

To solve the problem step by step, we will calculate the potential gradient across the potentiometer wire.

### Step 1: Calculate the total resistance in the circuit
The total resistance \( R_{total} \) in the circuit is the sum of the resistance of the potentiometer wire \( R_p \) and the series resistance \( R_s \):

\[ R_{total} = R_p + R_s = 20 \, \Omega + 480 \, \Omega = 500 \, \Omega \]
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