Current Electricity: PYQ Walkthrough (10)

easy • 2 min read
Tags Current Electricity

Question

(NEET 2023 pattern) A cell of EMF 66 V and internal resistance 0.50.5 Ω is connected to an external resistance of 5.55.5 Ω. Find the current in the circuit, the terminal voltage of the cell, and the power dissipated in the external resistor.

Solution — Step by Step

Total resistance =R+r=5.5+0.5=6= R + r = 5.5 + 0.5 = 6 Ω. The EMF drives the current through this total resistance.

I=εR+r=66=1 AI = \frac{\varepsilon}{R + r} = \frac{6}{6} = 1 \text{ A}

Terminal voltage is the voltage across the cell’s external terminals, which equals the EMF minus the drop across internal resistance:

V=ε−Ir=6−1×0.5=5.5 VV = \varepsilon - Ir = 6 - 1 \times 0.5 = 5.5 \text{ V}

Equivalently, V=IR=1×5.5=5.5V = IR = 1 \times 5.5 = 5.5 V — same answer, sanity check passes.

 P=I2R=12×5.5=5.5 WP = I^2 R = 1^2 \times 5.5 = 5.5 \text{ W}

Final Answer: I=1I = 1 A, V=5.5V = 5.5 V, P=5.5P = 5.5 W.

Why This Works

The cell’s EMF is its open-circuit voltage; once a current flows, some EMF is “lost” across the internal resistance, and only the rest appears across the external circuit. That’s why V<εV < \varepsilon for any finite current.

The two formulas V=ε−IrV = \varepsilon - Ir and V=IRV = IR must always agree. If they don’t, you have an arithmetic error somewhere — use this as a built-in check.

Alternative Method

We can use energy bookkeeping: power delivered by the cell =εI=6= \varepsilon I = 6 W. Power lost inside the cell =I2r=0.5= I^2 r = 0.5 W. Power in external R=6−0.5=5.5R = 6 - 0.5 = 5.5 W. Same answer, faster mental check.

Students often confuse EMF with terminal voltage. EMF ε\varepsilon is a property of the cell only; terminal voltage VV depends on the load. When a question says “voltage of the battery”, they usually mean terminal voltage VV, not EMF.

For maximum power transfer to the external load, R=rR = r. At that condition, V=ε/2V = \varepsilon/2 and Pmax=ε2/(4r)P_{\text{max}} = \varepsilon^2/(4r). NEET examiners love this corollary — keep it on your formula card.

Want to master this topic?

Read the complete guide with more examples and exam tips.

Go to full topic guide →

Try These Next

A 40W Bulb on 220V Supply — Find Current and Resistance

medium

A cell of emf 2V internal resistance 0.5Ω connected to 4.5Ω — find current and terminal voltage

hard

Current Electricity: Common Mistakes and Fixes (9)

hard

Current Electricity: Application Problems (1)

easy

Current Electricity: Conceptual Doubts Cleared (8)

medium