A voltmeter of resistance `R_(V)` and an ammeter of resistance `R_(A)` are connected in series across a battery of emf E and of negligible internal resistance . When a resistance R is connected in parallel to volmeter , reading of ammeter increases to three times while that of volmeter reduces to one - third. Calculate `R_(A)andR_(V)` in terms of R.

Explanation

To solve the problem, we need to analyze the circuit conditions before and after the resistance R is connected in parallel with the voltmeter. Let's break down the solution step by step.

### Step 1: Define the initial conditions
Initially, we have a voltmeter with resistance \( R_V \) and an ammeter with resistance \( R_A \) connected in series across a battery of EMF \( E \). The total resistance in the circuit is:
\[ R_{\text{total}} = R_A + R_V \]
The current \( I_1 \) flowing through the circuit can be expressed using Ohm's law:
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